theoretical problems. For this purpose, they can be defined as many different types which
suitably reflect the individual contexts of the represented problem. To address cutting-edge
problems based on graph data, the research field of Graph Neural Networks (GNNs) has
emerged. Despite the field’s youth and the speed at which new models are developed, many
recent surveys have been published to keep track of them. Nevertheless, it has not yet
been gathered which GNN can process what kind of graph types. In this survey, we give a
detailed overview of already existing GNNs and, unlike previous surveys, categorize them
according to their ability to handle different graph types and properties. We consider GNNs
operating on static and dynamic graphs of different structural constitutions, with or without
node or edge attributes. Moreover, we distinguish between GNN models for discrete-time or
continuous-time dynamic graphs and group the models according to their architecture. We
find that there are still graph types that are not or only rarely covered by existing GNN
models. We point out where models are missing and give potential reasons for their absence. ER - TY - CONF AU - Krompass, Denis AU - Nickel, Maximilian AU - Tresp, Volker A2 - T1 - Large-scale factorization of type-constrained multi-relational data T2 - International Conference on Data Science and Advanced Analytics, DSAA 2014, Shanghai, China, October 30 - November 1, 2014 PB - IEEE CY - PY - 2014/ M2 - VL - IS - SP - 18 EP - 24 UR - http://dx.doi.org/10.1109/DSAA.2014.7058046 M3 - 10.1109/DSAA.2014.7058046 KW - graph KW - knowledge KW - learning KW - toread L1 - SN - 978-1-4799-6991-3 N1 - dblp: BibTeX record conf/dsaa/KrompassNT14 N1 - AB - ER - TY - CONF AU - Doerfel, Stephan AU - Jäschke, Robert A2 - T1 - An analysis of tag-recommender evaluation procedures T2 - Proceedings of the 7th ACM conference on Recommender systems PB - ACM CY - New York, NY, USA PY - 2013/ M2 - VL - IS - SP - 343 EP - 346 UR - https://www.kde.cs.uni-kassel.de/pub/pdf/doerfel2013analysis.pdf M3 - 10.1145/2507157.2507222 KW - 2013 KW - bibsonomy KW - bookmarking KW - collaborative KW - core KW - evaluation KW - folkrank KW - folksonomy KW - graph KW - iteg KW - itegpub KW - l3s KW - recommender KW - social KW - tagging L1 - SN - 978-1-4503-2409-0 N1 - N1 - AB - Since the rise of collaborative tagging systems on the web, the tag recommendation task -- suggesting suitable tags to users of such systems while they add resources to their collection -- has been tackled. However, the (offline) evaluation of tag recommendation algorithms usually suffers from difficulties like the sparseness of the data or the cold start problem for new resources or users. Previous studies therefore often used so-called post-cores (specific subsets of the original datasets) for their experiments. In this paper, we conduct a large-scale experiment in which we analyze different tag recommendation algorithms on different cores of three real-world datasets. We show, that a recommender's performance depends on the particular core and explore correlations between performances on different cores. ER - TY - JOUR AU - Heidtmann, Klaus T1 - Internet-Graphen JO - Informatik-Spektrum PY - 2013/ VL - 36 IS - 5 SP - 440 EP - 448 UR - http://dx.doi.org/10.1007/s00287-012-0654-z M3 - 10.1007/s00287-012-0654-z KW - Graph KW - Graphen KW - Informatik KW - Informatik-Spektrum KW - Internet KW - Spektrum KW - graphs L1 - SN - N1 - Internet-Graphen - Springer N1 - AB - Bildeten die Keimzellen des Internet noch kleine und einfach strukturierte Netze, so vergrößerten sich sowohl seine physikalischen als auch seine logischen Topologien später rasant. Wuchs einerseits das Netz aus Rechnern als Knoten und Verbindungsleitungen als Kanten immer weiter, so bedienten sich andererseits gleichzeitig immer mehr Anwendungen dieser Infrastruktur, um darüber ihrerseits immer größere und komplexere virtuelle Netze zu weben, z. B. das WWW oder soziale Online-Netze. Auf jeder Ebene dieser Hierarchie lassen sich die jeweiligen Netztopologien mithilfe von Graphen beschreiben und so mathematisch untersuchen. So ergeben sich interessante Einblicke in die Struktureigenschaften unterschiedlicher Graphentypen, die großen Einfluss auf die Leistungsfähigkeit des Internet haben. Hierzu werden charakteristische Eigenschaften und entsprechende Kenngrößen verschiedener Graphentypen betrachtet wie der Knotengrad, die Durchschnittsdistanz, die Variation der Kantendichte in unterschiedlichen Netzteilen und die topologische Robustheit als Widerstandsfähigkeit gegenüber Ausfällen und Angriffen. Es wird dabei Bezug genommen auf analytische, simulative und zahlreiche empirische Untersuchungen des Internets und hingewiesen auf Simulationsprogramme sowie Abbildungen von Internetgraphen im Internet. ER - TY - JOUR AU - Landia, Nikolas AU - Doerfel, Stephan AU - Jäschke, Robert AU - Anand, Sarabjot Singh AU - Hotho, Andreas AU - Griffiths, Nathan T1 - Deeper Into the Folksonomy Graph: FolkRank Adaptations and Extensions for Improved Tag Recommendations JO - cs.IR PY - 2013/ VL - 1310.1498 IS - SP - EP - UR - http://arxiv.org/abs/1310.1498 M3 - KW - 2013 KW - bookmarking KW - collaborative KW - folkrank KW - folksonomy KW - graph KW - iteg KW - itegpub KW - l3s KW - recommender KW - social KW - tagging L1 - SN - N1 - N1 - AB - The information contained in social tagging systems is often modelled as a graph of connections between users, items and tags. Recommendation algorithms such as FolkRank, have the potential to leverage complex relationships in the data, corresponding to multiple hops in the graph. We present an in-depth analysis and evaluation of graph models for social tagging data and propose novel adaptations and extensions of FolkRank to improve tag recommendations. We highlight implicit assumptions made by the widely used folksonomy model, and propose an alternative and more accurate graph-representation of the data. Our extensions of FolkRank address the new item problem by incorporating content data into the algorithm, and significantly improve prediction results on unpruned datasets. Our adaptations address issues in the iterative weight spreading calculation that potentially hinder FolkRank's ability to leverage the deep graph as an information source. Moreover, we evaluate the benefit of considering each deeper level of the graph, and present important insights regarding the characteristics of social tagging data in general. Our results suggest that the base assumption made by conventional weight propagation methods, that closeness in the graph always implies a positive relationship, does not hold for the social tagging domain. ER - TY - JOUR AU - Landia, Nikolas AU - Doerfel, Stephan AU - Jäschke, Robert AU - Anand, Sarabjot Singh AU - Hotho, Andreas AU - Griffiths, Nathan T1 - Deeper Into the Folksonomy Graph: FolkRank Adaptations and Extensions for Improved Tag Recommendations JO - cs.IR PY - 2013/ VL - 1310.1498 IS - SP - EP - UR - http://arxiv.org/abs/1310.1498 M3 - KW - 2013 KW - bookmarking KW - collaborative KW - folkrank KW - folksonomy KW - graph KW - myown L1 - SN - N1 - N1 - AB - The information contained in social tagging systems is often modelled as a graph of connections between users, items and tags. Recommendation algorithms such as FolkRank, have the potential to leverage complex relationships in the data, corresponding to multiple hops in the graph. We present an in-depth analysis and evaluation of graph models for social tagging data and propose novel adaptations and extensions of FolkRank to improve tag recommendations. We highlight implicit assumptions made by the widely used folksonomy model, and propose an alternative and more accurate graph-representation of the data. Our extensions of FolkRank address the new item problem by incorporating content data into the algorithm, and significantly improve prediction results on unpruned datasets. Our adaptations address issues in the iterative weight spreading calculation that potentially hinder FolkRank's ability to leverage the deep graph as an information source. Moreover, we evaluate the benefit of considering each deeper level of the graph, and present important insights regarding the characteristics of social tagging data in general. Our results suggest that the base assumption made by conventional weight propagation methods, that closeness in the graph always implies a positive relationship, does not hold for the social tagging domain. ER - TY - JOUR AU - Landia, Nikolas AU - Doerfel, Stephan AU - Jäschke, Robert AU - Anand, Sarabjot Singh AU - Hotho, Andreas AU - Griffiths, Nathan T1 - Deeper Into the Folksonomy Graph: FolkRank Adaptations and Extensions for Improved Tag Recommendations JO - cs.IR PY - 2013/ VL - 1310.1498 IS - SP - EP - UR - http://arxiv.org/abs/1310.1498 M3 - KW - 2013 KW - bookmarking KW - collaborative KW - folkrank KW - folksonomy KW - graph KW - myown KW - recommender KW - social KW - tagging L1 - SN - N1 - N1 - AB - The information contained in social tagging systems is often modelled as a graph of connections between users, items and tags. Recommendation algorithms such as FolkRank, have the potential to leverage complex relationships in the data, corresponding to multiple hops in the graph. We present an in-depth analysis and evaluation of graph models for social tagging data and propose novel adaptations and extensions of FolkRank to improve tag recommendations. We highlight implicit assumptions made by the widely used folksonomy model, and propose an alternative and more accurate graph-representation of the data. Our extensions of FolkRank address the new item problem by incorporating content data into the algorithm, and significantly improve prediction results on unpruned datasets. Our adaptations address issues in the iterative weight spreading calculation that potentially hinder FolkRank's ability to leverage the deep graph as an information source. Moreover, we evaluate the benefit of considering each deeper level of the graph, and present important insights regarding the characteristics of social tagging data in general. Our results suggest that the base assumption made by conventional weight propagation methods, that closeness in the graph always implies a positive relationship, does not hold for the social tagging domain. ER - TY - JOUR AU - Liu, Xiaozhong AU - Zhang, Jinsong AU - Guo, Chun T1 - Full-Text Citation Analysis: A New Method to Enhance Scholarly Network JO - Journal of the American Society for Information Science and Technology PY - 2012/ VL - IS - SP - EP - UR - http://discern.uits.iu.edu:8790/publication/Full%20text%20citation.pdf M3 - KW - analysis KW - citation KW - classification KW - graph KW - pagerank KW - ranking KW - scientometrics KW - sota L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Liu, Xiaozhong AU - Zhang, Jinsong AU - Guo, Chun T1 - Full-Text Citation Analysis: A New Method to Enhance Scholarly Network JO - Journal of the American Society for Information Science and Technology PY - 2012/ VL - IS - SP - EP - UR - http://discern.uits.iu.edu:8790/publication/Full%20text%20citation.pdf M3 - KW - analysis KW - citation KW - classification KW - graph KW - pagerank KW - ranking KW - scientometrics KW - sota KW - topic L1 - SN - N1 - N1 - AB - ER - TY - CONF AU - Pereira Nunes, Bernardo AU - Kawase, Ricardo AU - Dietze, Stefan AU - Taibi, Davide AU - Casanova, Marco Antonio AU - Nejdl, Wolfgang A2 - Rizzo, Giuseppe A2 - Mendes, Pablo A2 - Charton, Eric A2 - Hellmann, Sebastian A2 - Kalyanpur, Aditya T1 - Can Entities be Friends? T2 - Proceedings of the Web of Linked Entities Workshop in conjuction with the 11th International Semantic Web Conference PB - CY - PY - 2012/november M2 - VL - 906 IS - SP - 45 EP - 57 UR - http://ceur-ws.org/Vol-906/paper6.pdf M3 - KW - data KW - detection KW - entity KW - graph KW - linked KW - relation KW - web L1 - SN - N1 - N1 - AB - The richness of the (Semantic) Web lies in its ability to link related resources as well as data across the Web. However, while relations within particular datasets are often well defined, links between disparate datasets and corpora of Web resources are rare. The increasingly widespread use of cross-domain reference datasets, such as Freebase and DBpedia for annotating and enriching datasets as well as document corpora, opens up opportunities to exploit their inherent semantics to uncover semantic relationships between disparate resources. In this paper, we present an approach to uncover relationships between disparate entities by analyzing the graphs of used reference datasets. We adapt a relationship assessment methodology from social network theory to measure the connectivity between entities in reference datasets and exploit these measures to identify correlated Web resources. Finally, we present an evaluation of our approach using the publicly available datasets Bibsonomy and USAToday. ER - TY - CONF AU - Pereira Nunes, Bernardo AU - Kawase, Ricardo AU - Dietze, Stefan AU - Taibi, Davide AU - Casanova, Marco Antonio AU - Nejdl, Wolfgang A2 - Rizzo, Giuseppe A2 - Mendes, Pablo A2 - Charton, Eric A2 - Hellmann, Sebastian A2 - Kalyanpur, Aditya T1 - Can Entities be Friends? T2 - Proceedings of the Web of Linked Entities Workshop in conjuction with the 11th International Semantic Web Conference PB - CY - PY - 2012/november M2 - VL - 906 IS - SP - 45 EP - 57 UR - http://ceur-ws.org/Vol-906/paper6.pdf M3 - KW - data KW - detection KW - entity KW - graph KW - linked KW - relation KW - web L1 - SN - N1 - N1 - AB - The richness of the (Semantic) Web lies in its ability to link related resources as well as data across the Web. However, while relations within particular datasets are often well defined, links between disparate datasets and corpora of Web resources are rare. The increasingly widespread use of cross-domain reference datasets, such as Freebase and DBpedia for annotating and enriching datasets as well as document corpora, opens up opportunities to exploit their inherent semantics to uncover semantic relationships between disparate resources. In this paper, we present an approach to uncover relationships between disparate entities by analyzing the graphs of used reference datasets. We adapt a relationship assessment methodology from social network theory to measure the connectivity between entities in reference datasets and exploit these measures to identify correlated Web resources. Finally, we present an evaluation of our approach using the publicly available datasets Bibsonomy and USAToday. ER - TY - JOUR AU - Batagelj, Vladimir AU - Zaveršnik, Matjaž T1 - Fast algorithms for determining (generalized) core groups in social networks JO - Advances in Data Analysis and Classification PY - 2011/ VL - 5 IS - 2 SP - 129 EP - 145 UR - http://dx.doi.org/10.1007/s11634-010-0079-y M3 - 10.1007/s11634-010-0079-y KW - core KW - graph L1 - SN - N1 - Advances in Data Analysis and Classification, Volume 5, Number 2 - SpringerLink N1 - AB - The structure of a large network (graph) can often be revealed by partitioning it into smaller and possibly more dense sub-networks that are easier to handle. One of such decompositions is based on “ k -cores”, proposed in 1983 by Seidman. Together with connectivity components, cores are one among few concepts that provide efficient decompositions of large graphs and networks. In this paper we propose an efficient algorithm for determining the cores decomposition of a given network with complexity $$O(m)$$, where m is the number of lines (edges or arcs). In the second part of the paper the classical concept of k -core is generalized in a way that uses a vertex property function instead of degree of a vertex. For local monotone vertex property functions the corresponding generalized cores can be determined in $$O(motn))$$ time, where n is the number of vertices and Δ is the maximum degree. Finally the proposed algorithms are illustrated by the analysis of a collaboration network in the field of computational geometry. ER - TY - GEN AU - Ugander, Johan AU - Karrer, Brian AU - Backstrom, Lars AU - Marlow, Cameron A2 - T1 - The Anatomy of the Facebook Social Graph JO - PB - AD - PY - 2011/ VL - IS - SP - EP - UR - http://arxiv.org/abs/1111.4503 M3 - KW - facebook KW - graph KW - network KW - social L1 - N1 - The Anatomy of the Facebook Social Graph N1 - AB - We study the structure of the social graph of active Facebook users, the
largest social network ever analyzed. We compute numerous features of the graph
including the number of users and friendships, the degree distribution, path
lengths, clustering, and mixing patterns. Our results center around three main
observations. First, we characterize the global structure of the graph,
determining that the social network is nearly fully connected, with 99.91% of
individuals belonging to a single large connected component, and we confirm the
"six degrees of separation" phenomenon on a global scale. Second, by studying
the average local clustering coefficient and degeneracy of graph neighborhoods,
we show that while the Facebook graph as a whole is clearly sparse, the graph
neighborhoods of users contain surprisingly dense structure. Third, we
characterize the assortativity patterns present in the graph by studying the
basic demographic and network properties of users. We observe clear degree
assortativity and characterize the extent to which "your friends have more
friends than you". Furthermore, we observe a strong effect of age on friendship
preferences as well as a globally modular community structure driven by
nationality, but we do not find any strong gender homophily. We compare our
results with those from smaller social networks and find mostly, but not
entirely, agreement on common structural network characteristics. ER - TY - JOUR AU - Chakrabarti, Soumen AU - Pathak, Amit AU - Gupta, Manish T1 - Index design and query processing for graph conductance search JO - The VLDB Journal PY - 2010/ VL - IS - SP - 1 EP - 26 UR - http://dx.doi.org/10.1007/s00778-010-0204-8 M3 - 10.1007/s00778-010-0204-8 KW - design KW - graph KW - index KW - interactive KW - pagerank KW - processing KW - query KW - toRead KW - folkrank L1 - SN - N1 - SpringerLink - The VLDB Journal, Online First™ N1 - AB - Graph conductance queries, also known as personalized PageRank and related to random walks with restarts, were originally proposed to assign a hyperlink-based prestige score to Web pages. More general forms of such queries are also very useful for ranking in entity-relation (ER) graphs used to represent relational, XML and hypertext data. Evaluation of PageRank usually involves a global eigen computation. If the graph is even moderately large, interactive response times may not be possible. Recently, the need for interactive PageRank evaluation has increased. The graph may be fully known only when the query is submitted. Browsing actions of the user may change some inputs to the PageRank computation dynamically. In this paper, we describe a system that analyzes query workloads and the ER graph, invests in limited offline indexing, and exploits those indices to achieve essentially constant-time query processing, even as the graph size scales. Our techniques—data and query statistics collection, index selection and materialization, and query-time index exploitation—have parallels in the extensive relational query optimization literature, but is applied to supporting novel graph data repositories. We report on experiments with five temporal snapshots of the CiteSeer ER graph having 74–702 thousand entity nodes, 0.17–1.16 million word nodes, 0.29–3.26 million edges between entities, and 3.29–32.8 million edges between words and entities. We also used two million actual queries from CiteSeer’s logs. Queries run 3–4 orders of magnitude faster than whole-graph PageRank, the gap growing with graph size. Index size is smaller than a text index. Ranking accuracy is 94–98% with reference to whole-graph PageRank. ER - TY - JOUR AU - Isella, Lorenzo AU - Stehlé, Juliette AU - Barrat, Alain AU - Cattuto, Ciro AU - Pinton, Jean-François AU - den Broeck, Wouter Van T1 - What's in a crowd? Analysis of face-to-face behavioral networks JO - CoRR PY - 2010/ VL - abs/1006.1260 IS - SP - EP - UR - http://dblp.uni-trier.de/db/journals/corr/corr1006.html#abs-1006-1260 M3 - KW - analysis KW - contact KW - crowd KW - graph KW - network KW - rfid KW - social KW - to KW - venus L1 - SN - N1 - N1 - AB - ER - TY - CONF AU - Mitzlaff, Folke AU - Benz, Dominik AU - Stumme, Gerd AU - Hotho, Andreas A2 - T1 - Visit me, click me, be my friend: An analysis of evidence networks of user relationships in Bibsonomy T2 - Proceedings of the 21st ACM conference on Hypertext and hypermedia PB - CY - Toronto, Canada PY - 2010/ M2 - VL - IS - SP - EP - UR - http://www.kde.cs.uni-kassel.de/pub/pdf/mitzlaff2010visit.pdf M3 - KW - 2010 KW - analysis KW - evidence_networks KW - graph KW - itegpub KW - myown KW - social_links KW - social_network KW - user_relationships L1 - SN - N1 - N1 - AB - ER - TY - CONF AU - Mitzlaff, Folke AU - Benz, Dominik AU - Stumme, Gerd AU - Hotho, Andreas A2 - T1 - Visit me, click me, be my friend: An analysis of evidence networks of user relationships in Bibsonomy T2 - Proceedings of the 21st ACM conference on Hypertext and hypermedia PB - CY - Toronto, Canada PY - 2010/ M2 - VL - IS - SP - EP - UR - http://www.kde.cs.uni-kassel.de/pub/pdf/mitzlaff2010visit.pdf M3 - KW - graph KW - social_links KW - social_network KW - myown KW - evidence_networks KW - 2010 KW - analysis KW - user_relationships KW - itegpub L1 - SN - N1 - N1 - AB - ER - TY - CONF AU - Akoglu, Leman AU - Faloutsos, Christos A2 - Buntine, Wray L. A2 - Grobelnik, Marko A2 - Mladenic, Dunja A2 - Shawe-Taylor, John T1 - RTG: A Recursive Realistic Graph Generator Using Random Typing. T2 - ECML/PKDD (1) PB - Springer CY - PY - 2009/ M2 - VL - 5781 IS - SP - 13 EP - 28 UR - http://dblp.uni-trier.de/db/conf/pkdd/pkdd2009-1.html#AkogluF09 M3 - KW - 2009 KW - ecml KW - generator KW - graph KW - law KW - pkdd KW - power KW - properties L1 - SN - 978-3-642-04179-2 N1 - N1 - AB - ER - TY - CONF AU - Berlingerio, Michele AU - Bonchi, Francesco AU - Bringmann, Björn AU - Gionis, Aristides A2 - Buntine, Wray L. A2 - Grobelnik, Marko A2 - Mladenic, Dunja A2 - Shawe-Taylor, John T1 - Mining Graph Evolution Rules. T2 - ECML/PKDD (1) PB - Springer CY - PY - 2009/ M2 - VL - 5781 IS - SP - 115 EP - 130 UR - http://dblp.uni-trier.de/db/conf/pkdd/pkdd2009-1.html#BerlingerioBBG09 M3 - KW - 2009 KW - ecml KW - evolution KW - generation KW - graph KW - pkdd KW - time L1 - SN - 978-3-642-04179-2 N1 - N1 - AB - ER - TY - JOUR AU - Fürnkranz, Johannes AU - Hüllermeier, Eyke AU - Vanderlooy, Stijn T1 - Binary Decomposition Methods for Multipartite Ranking JO - Machine Learning and Knowledge Discovery in Databases PY - 2009/ VL - IS - SP - 359 EP - 374 UR - http://dx.doi.org/10.1007/978-3-642-04180-8_41 M3 - KW - 2009 KW - ecml KW - graph KW - multipartite KW - pkdd KW - ranking L1 - SN - N1 - N1 - AB - Bipartite ranking refers to the problem of learning a ranking function from a training set of positively and negatively labeled
examples. Applied to a set of unlabeled instances, a ranking function is expected to establish a total order in which positiveinstances precede negative ones. The performance of a ranking function is typically measured in terms of the AUC. In thispaper, we study the problem of multipartite ranking, an extension of bipartite ranking to the multi-class case. In this regard,we discuss extensions of the AUC metric which are suitable as evaluation criteria for multipartite rankings. Moreover, tolearn multipartite ranking functions, we propose methods on the basis of binary decomposition techniques that have previouslybeen used for multi-class and ordinal classification. We compare these methods both analytically and experimentally, not onlyagainst each other but also to existing methods applicable to the same problem. ER - TY - JOUR AU - Gansner, Emden R. AU - Hu, Yifan AU - Kobourov, Stephen G. T1 - GMap: Drawing Graphs as Maps JO - cs.CG PY - 2009/07 VL - arXiv:0907.2585v1 IS - SP - EP - UR - http://arxiv.org/abs/0907.2585 M3 - KW - analysis KW - citation KW - drawing KW - gmap KW - graph KW - graphics KW - graphviz KW - network KW - sna KW - social KW - visualization L1 - SN - N1 - N1 - AB - Information visualization is essential in making sense out of large data sets. Often, high-dimensional data are visualized as a collection of points in 2-dimensional space through dimensionality reduction techniques. However, these traditional methods often do not capture well the underlying structural information, clustering, and neighborhoods. In this paper, we describe GMap: a practical tool for visualizing relational data with geographic-like maps. We illustrate the effectiveness of this approach with examples from several domains All the maps referenced in this paper can be found in http://www.research.att.com/~yifanhu/GMap ER - TY - GEN AU - Ghosh, Rumi AU - Lerman, Kristina A2 - T1 - Structure of Heterogeneous Networks JO - PB - AD - PY - 2009/ VL - IS - SP - EP - UR - http://arxiv.org/abs/0906.2212 M3 - KW - graph KW - graphs KW - heterogenous KW - measures KW - multi-mode KW - networks KW - sna L1 - N1 - [0906.2212] Structure of Heterogeneous Networks N1 - AB - Heterogeneous networks play a key role in the evolution of communities and
the decisions individuals make. These networks link different types of
entities, for example, people and the events they attend. Network analysis
algorithms usually project such networks unto simple graphs composed of
entities of a single type. In the process, they conflate relations between
entities of different types and loose important structural information. We
develop a mathematical framework that can be used to compactly represent and
analyze heterogeneous networks that combine multiple entity and link types. We
generalize Bonacich centrality, which measures connectivity between nodes by
the number of paths between them, to heterogeneous networks and use this
measure to study network structure. Specifically, we extend the popular
modularity-maximization method for community detection to use this centrality
metric. We also rank nodes based on their connectivity to other nodes. One
advantage of this centrality metric is that it has a tunable parameter we can
use to set the length scale of interactions. By studying how rankings change
with this parameter allows us to identify important nodes in the network. We
apply the proposed method to analyze the structure of several heterogeneous
networks. We show that exploiting additional sources of evidence corresponding
to links between, as well as among, different entity types yields new insights
into network structure.
ER - TY - CONF AU - Maes, Francis AU - Peters, Stéphane AU - Denoyer, Ludovic AU - Gallinari, Patrick A2 - Buntine, Wray L. A2 - Grobelnik, Marko A2 - Mladenic, Dunja A2 - Shawe-Taylor, John T1 - Simulated Iterative Classification A New Learning Procedure for Graph Labeling. T2 - ECML/PKDD (2) PB - Springer CY - PY - 2009/ M2 - VL - 5782 IS - SP - 47 EP - 62 UR - http://dblp.uni-trier.de/db/conf/pkdd/pkdd2009-2.html#MaesPDG09 M3 - KW - 2009 KW - classification KW - ecml KW - graph KW - iterative KW - label KW - labeling KW - multi KW - pkdd L1 - SN - 978-3-642-04173-0 N1 - N1 - AB - Collective classification refers to the classification of interlinked and relational objects described as nodes in a graph. The Iterative Classification Algorithm (ICA) is a simple, efficient and widely used method to solve this problem. It is representative of a family of methods for which inference proceeds as an iterative process: at each step, nodes of the graph are classified according to the current predicted labels of their neighbors. We show that learning in this class of models suffers from a training bias. We propose a new family of methods, called Simulated ICA, which helps reducing this training bias by simulating inference during learning. Several variants of the method are introduced. They are both simple, efficient and scale well. Experiments performed on a series of 7 datasets show that the proposed methods outperform representative state-of-the-art algorithms while keeping a low complexity. ER - TY - CONF AU - Murata, Tsuyoshi A2 - T1 - Modularities for Bipartite Networks T2 - HT '09: Proceedings of the Twentieth ACM Conference on Hypertext and Hypermedia PB - ACM CY - New York, NY, USA PY - 2009/07 M2 - VL - IS - SP - EP - UR - M3 - KW - ht09 KW - graph KW - bipartite L1 - SN - N1 - N1 - AB - Real-world relations are often represented as bipartite networks, such as paper-author networks and event-attendee networks. Extracting dense subnetworks (communities) from bipartite networks and evaluating their qualities are practically important research topics. As the attempts for evaluating divisions of bipartite networks, Guimera and Barber propose bipartite modularities. This paper discusses the properties of these bipartite modularities and proposes another bipartite modularity that allows one-to-many correspondence of communities of different vertex types. Preliminary experimental results for the bipartite modularities are also described. ER - TY - THES AU - Butler, S.K. T1 - Eigenvalues and Structures of Graphs PY - 2008/ PB - University of California, San Diego SP - EP - UR - M3 - KW - graph KW - spectral KW - theory L1 - N1 - N1 - AB - ER - TY - JOUR AU - Filippone, M. AU - Camastra, F. AU - Masulli, F. AU - Rovetta, S. T1 - A survey of kernel and spectral methods for clustering JO - Pattern recognition PY - 2008/ VL - 41 IS - 1 SP - 176 EP - 190 UR - M3 - KW - community KW - detection KW - graph KW - kernel KW - spectral KW - survey KW - theory L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Jackson, Matthew T1 - Average Distance, Diameter, and Clustering in Social Networks with Homophily JO - Internet and Network Economics PY - 2008/ VL - IS - SP - 4 EP - 11 UR - http://dx.doi.org/10.1007/978-3-540-92185-1_3 M3 - KW - generator KW - graph KW - homophily KW - properties L1 - SN - N1 - N1 - AB - I examine a random network model where nodes are categorized by type and linking probabilities can differ across types. I
show that as homophily increases (so that the probability to link to other nodes of the same type increases and the probabilityof linking to nodes of some other types decreases) the average distance and diameter of the network are unchanged, while theaverage clustering in the network increases. ER - TY - GEN AU - Nicosia, V. AU - Mangioni, G. AU - Carchiolo, V. AU - Malgeri, M. A2 - T1 - Extending the definition of modularity to directed graphs with
overlapping communities JO - PB - AD - PY - 2008/ VL - IS - SP - EP - UR - http://arxiv.org/abs/0801.1647 M3 - KW - COMMUNE KW - community KW - directed KW - graph KW - modularity KW - network KW - overlapping L1 - N1 - N1 - AB - Complex networks topologies present interesting and surprising properties,
such as community structures, which can be exploited to optimize communication,
to find new efficient and context-aware routing algorithms or simply to
understand the dynamics and meaning of relationships among nodes. Complex
networks are gaining more and more importance as a reference model and are a
powerful interpretation tool for many different kinds of natural, biological
and social networks, where directed relationships and contextual belonging of
nodes to many different communities is a matter of fact. This paper starts from
the definition of modularity function, given by M. Newman to evaluate the
goodness of network community decompositions, and extends it to the more
general case of directed graphs with overlapping community structures.
Interesting properties of the proposed extension are discussed, a method for
finding overlapping communities is proposed and results of its application to
benchmark case-studies are reported. We also propose a new dataset which could
be used as a reference benchmark for overlapping community structures
identification.
ER - TY - CONF AU - Symeonidis, Panagiotis AU - Nanopoulos, Alexandros AU - Manolopoulos, Yannis A2 - T1 - Tag recommendations based on tensor dimensionality reduction T2 - RecSys '08: Proceedings of the 2008 ACM conference on Recommender systems PB - ACM CY - New York, NY, USA PY - 2008/ M2 - VL - IS - SP - 43 EP - 50 UR - http://portal.acm.org/citation.cfm?id=1454017 M3 - http://doi.acm.org/10.1145/1454008.1454017 KW - community KW - detection KW - graph KW - recommender KW - spectral KW - tag KW - theory L1 - SN - 978-1-60558-093-7 N1 - N1 - AB - ER - TY - CONF AU - Baur, Michael AU - Gaertler, Marco AU - Görke, Robert AU - Krug, Marcus AU - Wagner, Dorothea A2 - T1 - Generating Graphs with Predefined k-Core Structure T2 - Proceedings of the European Conference of Complex Systems PB - CY - PY - 2007/october M2 - VL - IS - SP - EP - UR - http://i11www.ira.uka.de/extra/publications/bggkw-ggpcs-07.pdf M3 - KW - analysis KW - core KW - generator KW - graph KW - structure L1 - SN - N1 - N1 - AB - The modeling of realistic networks is of great importance for modern complex systems research. Previous procedures typically model the natural growth of networks by means of iteratively adding nodes, geometric positioning information, a definition of link connectivity based on the preference for nearest neighbors or already highly connected nodes, or combine several of these approaches. Our novel model is based on the well-know concept of k-cores, originally introduced in social network analysis. Recent studies exposed the significant k-core structure of several real world systems, e.g. the AS network of the Internet. We present a simple and efficient method for generating networks which strictly adhere to the characteristics of a given k-core structure, called core fingerprint. We show-case our algorithm in a comparative evaluation with two well-known AS network generators. ER - TY - CHAP AU - Brandes, Ulrik AU - Delling, Daniel AU - Gaertler, Marco AU - Görke, Robert AU - Hoefer, Martin AU - Nikoloski, Zoran AU - Wagner, Dorothea A2 - Brandstädt, Andreas A2 - Kratsch, Dieter A2 - Müller, Haiko T1 - On Finding Graph Clusterings with Maximum Modularity T2 - Graph-Theoretic Concepts in Computer Science PB - Springer CY - Berlin / Heidelberg PY - 2007/ VL - 4769 IS - SP - 121 EP - 132 UR - http://dx.doi.org/10.1007/978-3-540-74839-7_12 M3 - 10.1007/978-3-540-74839-7_12 KW - clustering KW - graph KW - modularity KW - theory L1 - SN - 978-3-540-74838-0 N1 - Abstract - SpringerLink N1 - AB - Modularity is a recently introduced quality measure for graph clusterings. It has immediately received considerable attention in several disciplines, and in particular in the complex systems literature, although its properties are not well understood. We study the problem of finding clusterings with maximum modularity, thus providing theoretical foundations for past and present work based on this measure. More precisely, we prove the conjectured hardness of maximizing modularity both in the general case and with the restriction to cuts, and give an Integer Linear Programming formulation. This is complemented by first insights into the behavior and performance of the commonly applied greedy agglomaration approach. ER - TY - JOUR AU - Luxburg, Ulrike T1 - A tutorial on spectral clustering JO - Statistics and Computing PY - 2007/ VL - 17 IS - 4 SP - 395 EP - 416 UR - http://portal.acm.org/citation.cfm?id=1288832 M3 - http://dx.doi.org/10.1007/s11222-007-9033-z KW - community KW - detection KW - graph KW - spectral KW - theory L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Schaeffer, S.E. T1 - Graph clustering JO - Computer Science Review PY - 2007/ VL - 1 IS - 1 SP - 27 EP - 64 UR - http://scholar.google.de/scholar.bib?q=info:-vQhplU2EFYJ:scholar.google.com/&output=citation&hl=de&as_sdt=2000&ct=citation&cd=0 M3 - KW - clustering KW - community KW - detection KW - graph L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Spielman, D.A. T1 - Spectral Graph Theory and its Applications JO - Foundations of Computer Science, 2007. FOCS '07. 48th Annual IEEE Symposium on PY - 2007/oct. VL - IS - SP - 29 EP - 38 UR - M3 - 10.1109/FOCS.2007.56 KW - graph KW - spectral KW - theory L1 - SN - N1 - N1 - AB - Spectral graph theory is the study of the eigenvalues and eigenvectors of matrices associated with graphs. In this tutorial, we will try to provide some intuition as to why these eigenvectors and eigenvalues have combinatorial significance, and will sitn'ey some of their applications. ER - TY - CONF AU - Zesch, Torsten AU - Gurevych, Iryna A2 - T1 - Analysis of the Wikipedia Category Graph for NLP Applications T2 - Proceedings of the TextGraphs-2 Workshop (NAACL-HLT) PB - Association for Computational Linguistics CY - Rochester PY - 2007/04 M2 - VL - IS - SP - 1 EP - 8 UR - http://acl.ldc.upenn.edu/W/W07/W07-02.pdf#page=11 M3 - KW - analysis KW - category KW - graph KW - language KW - natural KW - network KW - nlp KW - processing KW - wikipedia L1 - SN - N1 - N1 - AB - In this paper, we discuss two graphs in Wikipedia (i) the article graph, and (ii) the category graph. We perform a graph-theoretic analysis of the category graph, and show that it is a scale-free, small world graph like other well-known lexical semantic networks. We substantiate our findings by transferring semantic relatedness algorithms defined on WordNet to the Wikipedia category graph. To assess the usefulness of the category graph as an NLP resource, we analyze its coverage and the performance of the transferred semantic relatedness algorithms. ER - TY - UNPB AU - Butler, Steve A2 - T1 - Spectral Graph Theory: Applications of Courant Fischer PY - 2006/ SP - EP - UR - M3 - KW - graph KW - spectral KW - theory L1 - N1 - N1 - AB - ER - TY - UNPB AU - Butler, Steve A2 - T1 - Spectral Graph Theory: Cheeger constants and discrepancy PY - 2006/ SP - EP - UR - M3 - KW - graph KW - introduction KW - spectral KW - theory L1 - N1 - N1 - AB - ER - TY - UNPB AU - Butler, Steve A2 - T1 - Spectral Graph Theory: Three common spectra PY - 2006/ SP - EP - UR - M3 - KW - graph KW - introduction KW - spectral KW - theory L1 - N1 - N1 - AB - ER - TY - JOUR AU - Cantador, I. AU - Castells, P. T1 - Building Emergent Social Networks and Group Profiles by Semantic User Preference Clustering JO - PY - 2006/ VL - IS - SP - EP - UR - M3 - KW - clustering KW - community KW - detection KW - graph L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Frivolt, G. AU - Pok, O. T1 - Comparison of Graph Clustering Approaches JO - PY - 2006/ VL - IS - SP - EP - UR - M3 - KW - clustering KW - graph KW - survey L1 - SN - N1 - N1 - AB - ER - TY - CONF AU - Hotho, Andreas AU - Jäschke, Robert AU - Schmitz, Christoph AU - Stumme, Gerd A2 - Sure, York A2 - Domingue, John T1 - Information Retrieval in Folksonomies: Search and Ranking T2 - The Semantic Web: Research and Applications PB - Springer CY - Heidelberg PY - 2006/06 M2 - VL - 4011 IS - SP - 411 EP - 426 UR - M3 - KW - 2006 KW - folkrank KW - folksonomy KW - graph KW - iccs_example KW - information KW - l3s KW - mining KW - ol_web2.0 KW - pagerank KW - rank KW - ranking KW - retrieval KW - search KW - seminar2006 KW - testttag KW - trias_example KW - webzu KW - widely_related L1 - hotho2006information.pdf SN - N1 - N1 - AB - Social bookmark tools are rapidly emerging on the Web. In such systems users are setting up lightweight conceptual structures called folksonomies. The reason for their immediate success is the fact that no specific skills are needed for participating. At the moment, however, the information retrieval support is limited. We present a formal model and a new search algorithm for folksonomies,called FolkRank, that exploits the structure of the folksonomy. The proposed algorithm is also applied to findcommunities within the folksonomy and is used to structure search results. All findings are demonstrated on a large scale dataset. ER - TY - JOUR AU - Newman, M. E. J. T1 - Modularity and community structure in networks JO - Proceedings of the National Academy of Sciences PY - 2006/ VL - 103 IS - 23 SP - 8577 EP - 8582 UR - M3 - 10.1073/pnas.0601602103 KW - clustering KW - community KW - graph KW - modularity KW - network KW - structure L1 - SN - N1 - N1 - AB - Many networks of interest in the sciences, including social networks, computer networks, and metabolic and regulatory networks, are found to divide naturally into communities or modules. The problem of detecting and characterizing this community structure is one of the outstanding issues in the study of networked systems. One highly effective approach is the optimization of the quality function known as “modularity” over the possible divisions of a network. Here I show that the modularity can be expressed in terms of the eigenvectors of a characteristic matrix for the network, which I call the modularity matrix, and that this expression leads to a spectral algorithm for community detection that returns results of demonstrably higher quality than competing methods in shorter running times. I illustrate the method with applications to several published network data sets. ER - TY - JOUR AU - Newman, MEJ T1 - Finding community structure in networks using the eigenvectors of matrices JO - Physical Review E PY - 2006/ VL - 74 IS - 3 SP - EP - UR - M3 - KW - community KW - detection KW - graph KW - modularity KW - spectral KW - theory L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Newman, MEJ T1 - Modularity and community structure in networks JO - Proceedings of the National Academy of Sciences PY - 2006/ VL - 103 IS - 23 SP - 8577 EP - 8582 UR - M3 - KW - community KW - detection KW - graph KW - modularity KW - spectral KW - theory L1 - SN - N1 - N1 - AB - ER - TY - CONF AU - Schmitz, Christoph AU - Hotho, Andreas AU - Jäschke, Robert AU - Stumme, Gerd A2 - Sure, York A2 - Domingue, John T1 - Content Aggregation on Knowledge Bases using Graph Clustering T2 - The Semantic Web: Research and Applications PB - Springer CY - Heidelberg PY - 2006/ M2 - VL - 4011 IS - SP - 530 EP - 544 UR - http://www.kde.cs.uni-kassel.de/stumme/papers/2006/schmitz2006content.pdf M3 - KW - 2006 KW - aggregation KW - clustering KW - content KW - graph KW - itegpub KW - l3s KW - myown KW - nepomuk KW - ontologies KW - ontology KW - seminar2006 KW - theory L1 - SN - N1 - N1 - AB - Recently, research projects such as PADLR and SWAP
have developed tools like Edutella or Bibster, which are targeted at
establishing peer-to-peer knowledge management (P2PKM) systems. In
such a system, it is necessary to obtain provide brief semantic
descriptions of peers, so that routing algorithms or matchmaking
processes can make decisions about which communities peers should
belong to, or to which peers a given query should be forwarded.
This paper provides a graph clustering technique on
knowledge bases for that purpose. Using this clustering, we can show
that our strategy requires up to 58% fewer queries than the
baselines to yield full recall in a bibliographic P2PKM scenario. ER - TY - RPRT AU - Dhillon, Inderjit S. AU - Guan, Yuqiang AU - Kulis, Brian A2 - T1 - A Unified View of Kernel k-means, Spectral Clustering and Graph Cuts PB - University of Texas Dept. of Computer Science AD - PY - 2005/ VL - IS - TR-04-25 SP - EP - UR - http://www.cs.utexas.edu/ftp/pub/techreports/tr04-25.pdf M3 - KW - community KW - detection KW - graph KW - k-means KW - spectral KW - theory L1 - N1 - N1 - N1 - AB - Recently, a variety of clustering algorithms have been proposed to handle data that is not linearly separable. Spectral clustering and kernel k-means are two such methods that are seemingly quite different. In this paper, we show that a general weighted kernel k-means objective is mathematically equivalent to a weighted graph partitioning objective. Special cases of this graph partitioning objective include ratio cut, normalized cut and ratio association. Our equivalence has important consequences: the weighted kernel k-means algorithm may be used to directly optimize the graph partitioning objectives, and conversely, spectral methods may be used to optimize the weighted kernel k-means objective. Hence, in cases where eigenvector computation is prohibitive, we eliminate the need for any eigenvector computation for graph partitioning. Moreover, we show that the Kernighan-Lin objective can also be incorporated into our framework, leading to an incremental weighted kernel k-means algorithm for local optim ization of the objective. We further discuss the issue of convergence of weighted kernel k-means for an arbitrary graph affinity matrix and provide a number of experimental results. These results show that non-spectral methods for graph partitioning are as effective as spectral methods and can be used for problems such as image segmentation in addition to data clustering. ER - TY - JOUR AU - Dias, Vânia M.F. AU - de Figueiredo, Celina M.H. AU - Szwarcfiter, Jayme L. T1 - Generating bicliques of a graph in lexicographic order JO - Theoretical Computer Science PY - 2005/ VL - 337 IS - 1-3 SP - 240 EP - 248 UR - http://www.sciencedirect.com/science/article/B6V1G-4FD0HTT-3/2/7efa1ee4d7b4823c7315a58b94f2f280 M3 - DOI: 10.1016/j.tcs.2005.01.014 KW - conp KW - graph KW - independent KW - set KW - theory L1 - SN - N1 - N1 - AB - An independent set of a graph is a subset of pairwise non-adjacent vertices. A complete bipartite set B is a subset of vertices admitting a bipartition B=X[union or logical sum]Y, such that both X and Y are independent sets, and all vertices of X are adjacent to those of Y. If both X,Y[not equal to][empty set], then B is called proper. A biclique is a maximal proper complete bipartite set of a graph. We present an algorithm that generates all bicliques of a graph in lexicographic order, with polynomial-time delay between the output of two successive bicliques. We also show that there is no polynomial-time delay algorithm for generating all bicliques in reverse lexicographic order, unless P=NP. The methods are based on those by Johnson, Papadimitriou and Yannakakis, in the solution of these two problems for independent sets, instead of bicliques. ER - TY - BOOK AU - Diestel, Reinhard A2 - T1 - Graph Theory PB - Springer-Verlag Heidelberg, New York AD - PY - 2005/ VL - IS - SP - EP - UR - http://www.math.ubc.ca/~solymosi/2007/443/GraphTheoryIII.pdf M3 - KW - book KW - density KW - diesel KW - graph KW - theory L1 - SN - N1 - N1 - AB - ER - TY - CHAP AU - Lerner, Jürgen A2 - Brandes, Ulrik A2 - Erlebach, Thomas T1 - Role Assignments T2 - Network Analysis PB - Springer CY - Berlin / Heidelberg PY - 2005/ VL - 3418 IS - SP - 216 EP - 252 UR - http://dx.doi.org/10.1007/978-3-540-31955-9_9 M3 - 10.1007/978-3-540-31955-9_9 KW - assignments KW - graph KW - lerner KW - network KW - roles KW - sna KW - social KW - structural L1 - SN - N1 - SpringerLink - Abstract N1 - AB - 9.0. 9.0.1. Preliminaries 9.0.2. Role Graph 9.1. Structural Equivalence 9.1.1. Lattice of Equivalence Relations 9.1.2. Lattice of Structural Equivalences 9.1.3. Computation of Structural Equivalences 9.2. Regular Equivalence 9.2.1. Elementary Properties 9.2.2. Lattice Structure and Regular Interior 9.2.3. Computation of Regular Interior 9.2.4. The Role Assignment Problem 9.2.5. Existence of k-Role Assignments 9.3. Other Equivalences 9.3.1. Exact Role Assignments 9.3.2. Automorphic and Orbit Equivalence 9.3.3. Perfect Equivalence 9.3.4. Relative Regular Equivalence 9.4. Graphs with Multiple Relations 9.5. The Semigroup of a Graph 9.5.1. Winship-Pattison Role Equivalence 9.6. Chapter Notes ER - TY - JOUR AU - White, S. AU - Smyth, P. T1 - A spectral clustering approach to finding communities in graph JO - PY - 2005/ VL - IS - SP - EP - UR - M3 - KW - community KW - detection KW - graph KW - spectral KW - theory L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - An, Yuan AU - Janssen, Jeannette AU - Milios, Evangelos E. T1 - Characterizing and Mining the Citation Graph of the Computer Science Literature JO - Knowl. Inf. Syst. PY - 2004/november VL - 6 IS - SP - 664 EP - 678 UR - http://dx.doi.org/10.1007/s10115-003-0128-3 M3 - http://dx.doi.org/10.1007/s10115-003-0128-3 KW - 10th KW - Citation KW - characterizing KW - citation KW - computer KW - graph KW - mining L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Bollobás*, Béla AU - Riordan, Oliver T1 - The Diameter of a Scale-Free Random Graph JO - Combinatorica PY - 2004/01 VL - 24 IS - 1 SP - 5 EP - 34 UR - http://dx.doi.org/10.1007/s00493-004-0002-2 M3 - KW - diameter KW - distance KW - geodesic KW - graph KW - mean KW - random L1 - SN - N1 - N1 - AB - We consider a random graph process in which vertices are added to the graph one at a time and joined to a fixed number m of earlier vertices, where each earlier vertex is chosen with probability proportional to its degree. This process was introduced by Barabási and Albert [3], as a simple model of the growth of real-world graphs such as the world-wide web. Computer experiments presented by Barabási, Albert and Jeong [1,5] and heuristic arguments given by Newman, Strogatz and Watts [23] suggest that after n steps the resulting graph should have diameter approximately log n. We show that while this holds for m=1, for m=2 the diameter is asymptotically log n/log log n.
ER - ER - TY - JOUR AU - Drineas, P. AU - Frieze, A. AU - Kannan, R. AU - Vempala, S. AU - Vinay, V. T1 - Clustering large graphs via the singular value decomposition JO - Machine Learning PY - 2004/ VL - 56 IS - 1 SP - 9 EP - 33 UR - http://scholar.google.de/scholar.bib?q=info:gQY9HvWhsJcJ:scholar.google.com/&output=citation&hl=de&ct=citation&cd=0 M3 - KW - clustering KW - graph KW - svd KW - vldb L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Flake, G.W. AU - Tarjan, R.E. AU - Tsioutsiouliklis, K. T1 - Graph clustering and minimum cut trees JO - Internet Mathematics PY - 2004/ VL - 1 IS - 4 SP - 385 EP - 408 UR - http://scholar.google.de/scholar.bib?q=info:27hvFfjDdrkJ:scholar.google.com/&output=citation&hl=de&ct=citation&cd=6 M3 - KW - clustering KW - community KW - detection KW - graph L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Langville, A.N. AU - Meyer, C.D. T1 - Deeper inside pagerank JO - Internet Mathematics PY - 2004/ VL - 1 IS - 3 SP - 335 EP - 380 UR - http://scholar.google.de/scholar.bib?q=info:2bjOOHLGPW8J:scholar.google.com/&output=citation&hl=de&ct=citation&cd=0 M3 - KW - graph KW - pagerank L1 - SN - N1 - N1 - AB - ER - TY - GEN AU - Batagelj, V. AU - Zaversnik, M. A2 - T1 - An O(m) Algorithm for Cores Decomposition of Networks JO - PB - AD - PY - 2003/ VL - IS - SP - EP - UR - http://arxiv.org/abs/cs/0310049 M3 - KW - core KW - graph KW - network L1 - N1 - [cs/0310049] An O(m) Algorithm for Cores Decomposition of Networks N1 - AB - The structure of large networks can be revealed by partitioning them to
smaller parts, which are easier to handle. One of such decompositions is based
on $k$--cores, proposed in 1983 by Seidman. In the paper an efficient, $O(m)$,
$m$ is the number of lines, algorithm for determining the cores decomposition
of a given network is presented. ER - TY - JOUR AU - Brandes, U. AU - Gaertler, M. AU - Wagner, D. T1 - Experiments on graph clustering algorithms JO - Lecture notes in computer science PY - 2003/ VL - IS - SP - 568 EP - 579 UR - http://scholar.google.de/scholar.bib?q=info:gDNQfOoSm6cJ:scholar.google.com/&output=citation&hl=de&ct=citation&cd=2 M3 - KW - algorithm KW - clustering KW - community KW - detection KW - evaluation KW - graph L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Estrada, E. AU - Rodriguez-Velázquez, J.A. T1 - Spectral measures of bipartivity in complex networks JO - SIAM Rev Phys Rev E PY - 2003/ VL - 72 IS - SP - EP - UR - M3 - KW - bipartite KW - community KW - detection KW - graph KW - modularity KW - spectral KW - theory L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Haveliwala, T.H. AU - Kamvar, S.D. T1 - The second eigenvalue of the Google matrix JO - A Stanford University Technical Report http://dbpubs. stanford. edu PY - 2003/ VL - IS - SP - EP - UR - M3 - KW - graph KW - pagerank KW - spectral KW - theory L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Newman, M. E. J. T1 - The structure and function of complex networks JO - SIAM Review PY - 2003/ VL - 45 IS - 2 SP - 167 EP - 256 UR - M3 - KW - graph KW - introduction KW - network KW - review KW - survey KW - theory L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Verma, D. AU - Meila, M. T1 - A comparison of spectral clustering algorithms JO - University of Washington, Tech. Rep. UW-CSE-03-05-01 PY - 2003/ VL - IS - SP - EP - UR - M3 - KW - community KW - detection KW - graph KW - spectral KW - theory L1 - SN - N1 - N1 - AB - ER - TY - CONF AU - Yu, Stella X. AU - Shi, Jianbo A2 - T1 - Multiclass Spectral Clustering T2 - Proc. International Conference on Computer Vision (ICCV 03) PB - CY - Nice, France PY - 2003/october M2 - VL - IS - SP - EP - UR - M3 - KW - Spectral KW - graph KW - partitioning KW - theory L1 - SN - N1 - N1 - AB - ER - TY - UNPB AU - Blelloch, Guy A2 - T1 - Graph Separators PY - 2002/ SP - EP - UR - M3 - KW - graph KW - separators KW - theory L1 - N1 - N1 - AB - ER - TY - CONF AU - Brandes, U. AU - Willhalm, T. A2 - T1 - Visualization of bibliographic networks with a reshaped landscape metaphor T2 - Proceedings of the symposium on Data Visualisation 2002 PB - Eurographics Association CY - Aire-la-Ville, Switzerland, Switzerland PY - 2002/ M2 - VL - IS - SP - 159 EP - ff UR - http://portal.acm.org/citation.cfm?id=509740.509765 M3 - KW - bibliographic KW - bibliography KW - citation KW - graph KW - networks KW - sna L1 - SN - 1-58113-536-X N1 - Visualization of bibliographic networks with a reshaped landscape metaphor N1 - AB - We describe a novel approach to visualize bibliographic networks that facilitates the simultaneous identification of clusters (e.g., topic areas) and prominent entities (e.g., surveys or landmark papers). While employing the landscape metaphor proposed in several earlier works, we introduce new means to determine relevant parameters of the landscape. Moreover, we are able to compute prominent entities, clustering of entities, and the landscape's surface in a surprisingly simple and uniform way. The effectiveness of our network visualizations is illustrated on data from the graph drawing literature. ER - TY - JOUR AU - Snijders, T.A.B. T1 - Markov chain Monte Carlo estimation of exponential random graph models JO - Journal of Social Structure PY - 2002/ VL - 3 IS - 2 SP - 1 EP - 40 UR - M3 - KW - carlo KW - estimation KW - exponential KW - generation KW - graph KW - model KW - monte KW - p* KW - parameter KW - sna L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Soderberg, B. T1 - General formalism for inhomogeneous random graphs JO - Phys. Rev. E PY - 2002/ VL - 66 IS - 6 SP - EP - UR - M3 - KW - graph KW - k-partite KW - random KW - theory L1 - SN - N1 - N1 - AB - ER - TY - CONF AU - Dhillon, Inderjit S. A2 - T1 - Co-clustering documents and words using bipartite spectral graph partitioning T2 - KDD '01: Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining PB - ACM Press CY - New York, NY, USA PY - 2001/ M2 - VL - IS - SP - 269 EP - 274 UR - http://portal.acm.org/citation.cfm?id=502512.502550 M3 - 10.1145/502512.502550 KW - community KW - detection KW - graph KW - spectral KW - theory L1 - SN - 158113391X N1 - N1 - AB - ER - TY - GEN AU - Monien, B. A2 - T1 - On Spectral Bounds for the k-Partitioning of Graphs JO - PB - AD - PY - 2001/ VL - IS - SP - EP - UR - M3 - KW - graph KW - spectral KW - theory L1 - N1 - N1 - AB - ER - TY - JOUR AU - Newman, MEJ AU - Strogatz, SH AU - Watts, DJ T1 - Random graphs with arbitrary degree distributions and their applications JO - Arxiv preprint cond-mat/0007235 PY - 2001/ VL - IS - SP - EP - UR - M3 - KW - configuration KW - degree KW - distribution KW - function KW - generating KW - graph KW - model KW - random L1 - SN - N1 - N1 - AB - ER - TY - CONF AU - Ng, Andrew Y. AU - Jordan, Michael I. AU - Weiss, Yair A2 - T1 - On spectral clustering: Analysis and an algorithm T2 - Advances in Neural Information Processing Systems 14 PB - MIT Press CY - PY - 2001/ M2 - VL - IS - SP - 849 EP - 856 UR - M3 - KW - clustering KW - community KW - detection KW - graph KW - spectral KW - theory L1 - SN - N1 - N1 - AB - Despite many empirical successes of spectral clustering methods| algorithms that cluster points using eigenvectors of matrices derived from the data|there are several unresolved issues. First, there are a wide variety of algorithms that use the eigenvectors in slightly dierent ways. Second, many of these algorithms have no proof that they will actually compute a reasonable clustering. In this paper, we present a simple spectral clustering algorithm that can be implemented using a few lines of Matlab. Using tools from matrix perturbation theory, we analyze the algorithm, and give conditions under which it can be expected to do well. We also show surprisingly good experimental results on a number of challenging clustering problems. 1 ER - TY - JOUR AU - Aiello, W. AU - Chung, F. AU - Lu, L. T1 - A random graph model for massive graphs JO - PY - 2000/ VL - IS - SP - 171 EP - 180 UR - http://scholar.google.de/scholar.bib?q=info:iG723gINfRAJ:scholar.google.com/&output=citation&hl=de&ct=citation&cd=0 M3 - KW - graph KW - pagerank KW - random KW - simrank KW - surfer L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Butler, S. T1 - Cospectral graphs for both the adjacency and normalized Laplacian matrices JO - PY - 2000/ VL - IS - SP - EP - UR - M3 - KW - bipartite KW - graph KW - spectral KW - theory L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Gansner, Emden R. AU - North, Stephen C. T1 - An open graph visualization system and its applications to software engineering JO - Software Practice & Experience PY - 2000/10 VL - 30 IS - 11 SP - 1203 EP - 1233 UR - http://dl.acm.org/citation.cfm?id=358668.358697 M3 - 10.1002/1097-024X(200009)30:11<1203::AID-SPE338>3.3.CO;2-E KW - drawing KW - graph KW - graphics KW - graphviz KW - visualization L1 - SN - N1 - N1 - AB - We describe a package of practical tools and libraries for manipulating graphs and their drawings. Our design, which aimed at facilitating the combination of the package components with other tools, includes stream and event interfaces for graph operations, high-quality static and dynamic layout algorithms, and the ability to handle sizable graphs. We conclude with a description of the applications of this package to a variety of software engineering tools. ER - TY - BOOK AU - Janson, Svante AU - Luczak, Tomasz AU - Rucinski, Andrzej A2 - T1 - Theory of random graphs PB - John Wiley & Sons AD - New York; Chichester PY - 2000/ VL - IS - SP - EP - UR - http://www.amazon.com/Random-Graphs-Svante-Janson/dp/0471175412 M3 - KW - density KW - graph KW - random L1 - SN - 0471175412 9780471175414 N1 - Random Graphs: Svante Janson, Tomasz Luczak, Andrzej Rucinski: 9780471175414: Amazon.com: Books N1 - AB - ER - TY - UNPB AU - Ranade, A.G. A2 - T1 - Some uses of spectral methods PY - 2000/ SP - EP - UR - M3 - KW - clustering KW - graph KW - spectral KW - svd KW - theory L1 - N1 - N1 - AB - ER - TY - JOUR AU - Anderson, C.J. AU - Wasserman, S. AU - Crouch, B. T1 - A p* primer: Logit models for social networks JO - Social Networks PY - 1999/ VL - 21 IS - 1 SP - 37 EP - 66 UR - M3 - KW - carlo KW - exponential KW - generation KW - graph KW - model KW - monte KW - random KW - simulation KW - sna L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Barabasi, A. L. AU - Albert, R. T1 - Emergence of scaling in random networks JO - Science PY - 1999/october VL - 286 IS - 5439 SP - 509 EP - 512 UR - http://view.ncbi.nlm.nih.gov/pubmed/10521342 M3 - KW - graph KW - network KW - properties KW - statistics L1 - SN - N1 - N1 - AB - Systems as diverse as genetic networks or the World Wide Web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature was found to be a consequence of two generic mechanisms: (i) networks expand continuously by the addition of new vertices, and (ii) new vertices attach preferentially to sites that are already well connected. A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems. ER - TY - CHAP AU - Batagelj, Vladimir AU - Mrvar, Andrej AU - Zaveršnik, Matjaž A2 - Kratochvíyl, Jan T1 - Partitioning Approach to Visualization of Large Graphs T2 - Graph Drawing PB - Springer CY - Berlin / Heidelberg PY - 1999/ VL - 1731 IS - SP - 90 EP - 97 UR - http://dx.doi.org/10.1007/3-540-46648-7_9 M3 - 10.1007/3-540-46648-7_9 KW - core KW - graph L1 - SN - 978-3-540-66904-3 N1 - Abstract - SpringerLink N1 - AB - The structure of large graphs can be revealed by partitioning graphs to smaller parts, which are easier to handle. In the paper we propose the use of core decomposition as an efficient approach for partitioning large graphs. On the selected subgraphs, computationally more intensive, clustering and blockmodeling can be used to analyze their internal structure. The approach is illustrated by an analysis of Snyder & Kick’s world trade graph. ER - TY - CONF AU - Brin, Sergey AU - Page, Lawrence A2 - T1 - The Anatomy of a Large-Scale Hypertextual Web Search Engine T2 - Computer Networks and ISDN Systems PB - CY - PY - 1998/ M2 - VL - IS - SP - 107 EP - 117 UR - http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.42.3243 M3 - KW - graph KW - pagerank L1 - SN - N1 - N1 - AB - In this paper, we present Google, a prototype of a large-scale search engine which makes heavy use of the structure present in hypertext. Google is designed to crawl and index the Web efficiently and produce much more satisfying search results than existing systems. The prototype with a full text and hyperlink database of at least 24 million pages is available at http://infolab.stanford.edu/~backrub/google.html To engineer a search engine is a challenging task. Search engines index tens to hundreds of millions of web pages involving a comparable number of distinct terms. They answer tens of millions of queries every day. Despite the importance of large-scale search engines on the web, very little academic research has been done on them. Furthermore, due to rapid advance in technology and web proliferation, creating a web search engine today is very different from three years ago. This paper provides an in-depth description of our large-scale web search engine -- the first such detailed public description w... ER - TY - JOUR AU - Guattery, S. AU - Miller, G.L. T1 - On the quality of spectral separators JO - SIAM Journal on Matrix Analysis and Applications PY - 1998/ VL - 19 IS - 3 SP - 701 EP - 719 UR - M3 - KW - graph KW - spectral KW - theory L1 - SN - N1 - N1 - AB - ER - TY - CONF AU - Karypis, George AU - Kumar, Vipin A2 - T1 - Multilevel k-way Hypergraph Partitioning T2 - In Proceedings of the Design and Automation Conference PB - CY - PY - 1998/ M2 - VL - IS - SP - 343 EP - 348 UR - M3 - KW - clustering KW - community KW - detection KW - graph KW - hypergraph KW - partitioning L1 - SN - N1 - N1 - AB - In this paper, we present a new multilevel k-way hypergraph partitioning algorithm that substantially outperforms the existing state-of-the-art K-PM/LR algorithm for multi-way partitioning. both for optimizing local as well as global objectives. Experiments on the ISPD98 benchmark suite show that the partitionings produced by our scheme are on the average 15% to 23% better than those produced by the K-PM/LR algorithm, both in terms of the hyperedge cut as well as the (K - 1) metric. Furthermore, our algorithm is significantly faster, requiring 4 to 5 times less time than that required by K-PM/LR. 1 Introduction Hypergraph partitioning is an important problem with extensive application to many areas, including VLSI design [10], efficient storage of large databases on disks [14], and data mining [13]. The problem is to partition the vertices of a hypergraph into k roughly equal parts, such that a certain objective function defined over the hyperedges is optimized. A commonly used obje... ER - TY - BOOK AU - Chung, F. R. K. A2 - T1 - Spectral Graph Theory PB - American Mathematical Society AD - PY - 1997/ VL - IS - SP - EP - UR - M3 - KW - graph KW - spectral KW - theory L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Karypis, G. AU - Aggarwal, R. AU - Kumar, V. AU - Shekhar, S. T1 - Multilevel hypergraph partitioning: Application in VLSI domain JO - PY - 1997/ VL - IS - SP - 526 EP - 529 UR - M3 - KW - clustering KW - community KW - detection KW - graph KW - hypergraph L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Mohar, B. T1 - Some applications of Laplace eigenvalues of graphs JO - Graph Symmetry: Algebraic Methods and Applications PY - 1997/ VL - 497 IS - SP - 227 EP - 275 UR - M3 - KW - graph KW - laplacian KW - spectral KW - survey KW - theory L1 - SN - N1 - N1 - AB - ER - TY - RPRT AU - Spielman, Daniel A. AU - Teng, Shang A2 - T1 - Spectral Partitioning Works: Planar Graphs and Finite Element Meshes PB - AD - Berkeley, CA, USA PY - 1996/ VL - IS - SP - EP - UR - M3 - KW - clustering KW - community KW - detection KW - graph KW - spectral KW - survey KW - theory L1 - N1 - N1 - N1 - AB - ER - TY - CONF AU - Alpert, Charles J. AU - Kahng, Andrew B. AU - zen Yao, So A2 - T1 - Spectral partitioning: The more eigenvectors, the better T2 - Proc. ACM/IEEE Design Automation Conf PB - CY - PY - 1995/ M2 - VL - IS - SP - 195 EP - 200 UR - M3 - KW - community KW - detection KW - graph KW - spectral KW - theory L1 - SN - N1 - N1 - AB - ER - TY - GEN AU - Molloy, M. AU - Reed, B. A2 - T1 - A critical point for random graphs with a given degree sequence JO - Random Structures & Algorithms PB - AD - PY - 1995/ VL - 6 IS - SP - 161 EP - 179 UR - /brokenurl#citeseer.ist.psu.edu/molloy95critical.html M3 - KW - component KW - configuration KW - giant KW - graph KW - model KW - random KW - theory L1 - N1 - N1 - AB - ER - TY - JOUR AU - Bolla, Marianna AU - Tusnády, Gábor T1 - Spectra and optimal partitions of weighted graphs JO - Discrete Math. PY - 1994/ VL - 128 IS - 1-3 SP - 1 EP - 20 UR - http://portal.acm.org/citation.cfm?id=179357.179359 M3 - http://dx.doi.org/10.1016/0012-365X(94)90100-7 KW - graph KW - spectral KW - the L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Chan, Pak K. AU - Schlag, Martine D. F. AU - Zien, Jason Y. T1 - Spectral K-way ratio-cut partitioning and clustering. JO - IEEE Trans. on CAD of Integrated Circuits and Systems PY - 1994/ VL - 13 IS - 9 SP - 1088 EP - 1096 UR - http://dblp.uni-trier.de/db/journals/tcad/tcad13.html#ChanSZ94 M3 - KW - community KW - detection KW - graph KW - partitioning KW - spectral KW - theory L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Hagen, Lars W. AU - Kahng, Andrew B. T1 - New spectral methods for ratio cut partitioning and clustering. JO - IEEE Trans. on CAD of Integrated Circuits and Systems PY - 1992/ VL - 11 IS - 9 SP - 1074 EP - 1085 UR - http://dblp.uni-trier.de/db/journals/tcad/tcad11.html#HagenK92 M3 - KW - graph KW - partitioning KW - spectral KW - theory L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Mohar, B. T1 - The Laplacian spectrum of graphs JO - Graph Theory, Combinatorics, and Applications PY - 1991/ VL - 2 IS - SP - 871 EP - 898 UR - M3 - KW - graph KW - laplacian KW - spectral KW - survey KW - theory L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Pothen, A. AU - Simon, H.D. AU - Liou, K.P. T1 - Partitioning Sparse Matrices with Eigenvectors of Graphs JO - SIAM J. MATRIX ANAL. APPLIC. PY - 1990/ VL - 11 IS - 3 SP - 430 EP - 452 UR - http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19970011963_1997016998.pdf M3 - KW - clustering KW - community KW - graph KW - partitioning KW - spectral KW - theory L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Frank, O. T1 - Random sampling and social networks: a survey of various approaches JO - Math. Sci. Humaines PY - 1988/ VL - 104 IS - SP - 19 EP - 33 UR - M3 - KW - graph KW - random KW - review KW - sna KW - theory L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Johnson, David S. AU - Papadimitriou, Christos H. T1 - On generating all maximal independent sets JO - Inf. Process. Lett. PY - 1988/ VL - 27 IS - 3 SP - 119 EP - 123 UR - http://portal.acm.org/citation.cfm?id=46241.46243 M3 - http://dx.doi.org/10.1016/0020-0190(88)90065-8 KW - complexity KW - graph KW - independent KW - sets KW - theory L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Seidman, Stephen B. T1 - Network structure and minimum degree JO - Social Networks PY - 1983/ VL - 5 IS - 3 SP - 269 EP - 287 UR - http://www.sciencedirect.com/science/article/pii/037887338390028X M3 - 10.1016/0378-8733(83)90028-X KW - core KW - graph KW - network L1 - SN - N1 - ScienceDirect.com - Social Networks - Network structure and minimum degree N1 - AB - Social network researchers have long sought measures of network cohesion, Density has often been used for this purpose, despite its generally admitted deficiencies. An approach to network cohesion is proposed that is based on minimum degree and which produces a sequence of subgraphs of gradually increasing cohesion. The approach also associates with any network measures of local density which promise to be useful both in characterizing network structures and in comparing networks. ER - TY - JOUR AU - Karonski, M. T1 - A review of random graphs JO - Journal of Graph Theory PY - 1982/ VL - 6 IS - 4 SP - EP - UR - M3 - KW - graph KW - random KW - theory L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Bollobas, B. T1 - The diameter of random graphs JO - Transactions of the American Mathematical Society PY - 1981/ VL - IS - SP - 41 EP - 52 UR - M3 - KW - diameter KW - graph KW - random L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Freeman, Linton C. T1 - A Set of Measures of Centrality Based on Betweenness JO - Sociometry PY - 1977/03 VL - 40 IS - 1 SP - 35 EP - 41 UR - http://links.jstor.org/sici?sici=0038-0431\%28197703\%2940\%3A1\%3C35\%3AASOMOC\%3E2.0.CO\%3B2-H M3 - KW - betweeness KW - centrality KW - graph KW - sna KW - theory L1 - SN - N1 - N1 - AB - A Family of new measures of point and graph centrality based on early intuitions of Bavelas (1948) is introduced. These measures define centrality in terms of the degree to which a point falls on the shortest path between others and therefore has a potential for control of communication. They may be used to index centrality in any large or small network of symmetrical relations, whether connected or unconnected. ER - TY - JOUR AU - Fiedler, M. T1 - A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory JO - Czechoslovak Mathematical Journal PY - 1975/ VL - 25 IS - 100 SP - 619 EP - 633 UR - M3 - KW - graph KW - spectral KW - theory L1 - SN - N1 - N1 - AB - ER - TY - JOUR AU - Donath, W.E. AU - Hoffman, A.J. T1 - Lower bounds for the partitioning of graphs JO - IBM Journal of Research and Development PY - 1973/ VL - 17 IS - 5 SP - 420 EP - 425 UR - M3 - KW - clustering KW - community KW - detection KW - graph KW - spectral KW - theory L1 - SN - N1 - N1 - AB - ER -