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.

@article{noKey, author = {Heidtmann, Klaus}, title = {Internet-Graphen}, journal = {Informatik-Spektrum}, publisher = {Springer Berlin Heidelberg}, year = {2013}, volume = {36}, number = {5}, pages = {440-448}, url = {http://dx.doi.org/10.1007/s00287-012-0654-z}, doi = {10.1007/s00287-012-0654-z}, issn = {0170-6012}, keywords = {Graph, Graphen, Informatik, Informatik-Spektrum, Internet, Spektrum, graphs}, abstract = {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. } }

%0 = article %A = Heidtmann, Klaus %D = 2013 %I = Springer Berlin Heidelberg %T = Internet-Graphen %U = http://dx.doi.org/10.1007/s00287-012-0654-z

Network science is an interdisciplinary endeavor, with methods and applications drawn from across the natural, social, and information sciences. A prominent problem in network science is the algorithmic detection of tightly connected groups of nodes known as communities. We developed a generalized framework of network quality functions that allowed us to study the community structure of arbitrary multislice networks, which are combinations of individual networks coupled through links that connect each node in one network slice to itself in other slices. This framework allows studies of community structure in a general setting encompassing networks that evolve over time, have multiple types of links (multiplexity), and have multiple scales.

@article{Mucha14052010, author = {Mucha, Peter J. and Richardson, Thomas and Macon, Kevin and Porter, Mason A. and Onnela, Jukka-Pekka}, title = {Community Structure in Time-Dependent, Multiscale, and Multiplex Networks}, journal = {Science}, year = {2010}, volume = {328}, number = {5980}, pages = {876-878}, url = {http://www.sciencemag.org/content/328/5980/876.abstract}, doi = {10.1126/science.1184819}, keywords = {communities, community, evolving, graphs, networks, time}, abstract = {Network science is an interdisciplinary endeavor, with methods and applications drawn from across the natural, social, and information sciences. A prominent problem in network science is the algorithmic detection of tightly connected groups of nodes known as communities. We developed a generalized framework of network quality functions that allowed us to study the community structure of arbitrary multislice networks, which are combinations of individual networks coupled through links that connect each node in one network slice to itself in other slices. This framework allows studies of community structure in a general setting encompassing networks that evolve over time, have multiple types of links (multiplexity), and have multiple scales.} }

%0 = article %A = Mucha, Peter J. and Richardson, Thomas and Macon, Kevin and Porter, Mason A. and Onnela, Jukka-Pekka %D = 2010 %T = Community Structure in Time-Dependent, Multiscale, and Multiplex Networks %U = http://www.sciencemag.org/content/328/5980/876.abstract

Heterogeneous networks play a key role in the evolution of communities and
e decisions individuals make. These networks link different types of
tities, for example, people and the events they attend. Network analysis
gorithms usually project such networks unto simple graphs composed of
tities of a single type. In the process, they conflate relations between
tities of different types and loose important structural information. We
velop a mathematical framework that can be used to compactly represent and
alyze heterogeneous networks that combine multiple entity and link types. We
neralize Bonacich centrality, which measures connectivity between nodes by
e number of paths between them, to heterogeneous networks and use this
asure to study network structure. Specifically, we extend the popular
dularity-maximization method for community detection to use this centrality
tric. We also rank nodes based on their connectivity to other nodes. One
vantage of this centrality metric is that it has a tunable parameter we can
e to set the length scale of interactions. By studying how rankings change
th this parameter allows us to identify important nodes in the network. We
ply the proposed method to analyze the structure of several heterogeneous
tworks. We show that exploiting additional sources of evidence corresponding
links between, as well as among, different entity types yields new insights
to network structure.

@misc{Ghosh2009, author = {Ghosh, Rumi and Lerman, Kristina}, title = {Structure of Heterogeneous Networks}, year = {2009}, note = {cite arxiv:0906.2212
}, url = {http://arxiv.org/abs/0906.2212}, keywords = {graph, graphs, heterogenous, measures, multi-mode, networks, sna}, abstract = { Heterogeneous networks play a key role in the evolution of communities andthe decisions individuals make. These networks link different types ofentities, for example, people and the events they attend. Network analysisalgorithms usually project such networks unto simple graphs composed ofentities of a single type. In the process, they conflate relations betweenentities of different types and loose important structural information. Wedevelop a mathematical framework that can be used to compactly represent andanalyze heterogeneous networks that combine multiple entity and link types. Wegeneralize Bonacich centrality, which measures connectivity between nodes bythe number of paths between them, to heterogeneous networks and use thismeasure to study network structure. Specifically, we extend the popularmodularity-maximization method for community detection to use this centralitymetric. We also rank nodes based on their connectivity to other nodes. Oneadvantage of this centrality metric is that it has a tunable parameter we canuse to set the length scale of interactions. By studying how rankings changewith this parameter allows us to identify important nodes in the network. Weapply the proposed method to analyze the structure of several heterogeneousnetworks. We show that exploiting additional sources of evidence correspondingto links between, as well as among, different entity types yields new insightsinto network structure.} }

%0 = misc %A = Ghosh, Rumi and Lerman, Kristina %B = } %C = %D = 2009 %I = %T = Structure of Heterogeneous Networks} %U = http://arxiv.org/abs/0906.2212

Mining graph data is an active research area. Several data mining methods and algorithms have been proposed to identify structures from graphs; still, the evaluation of those results is lacking. Within the framework of statistical hypothesis testing, we focus in this paper on randomization techniques for unweighted undirected graphs. Randomization is an important approach to assess the statistical significance of data mining results. Given an input graph, our randomization method will sample data from the class of graphs that share certain structural properties with the input graph. Here we describe three alternative algorithms based on local edge swapping and Metropolis sampling. We test our framework with various graph data sets and mining algorithms for two applications, namely graph clustering and frequent subgraph mining.

@article{Hanhijärvi2009, author = {Hanhijärvi, Sami and Garriga, Gemma and Puolamäki, Kai}, title = {Randomization techniques for graphs}, year = {2009}, url = {http://eprints.pascal-network.org/archive/00004486/}, keywords = {graphs, randomization, toRead}, abstract = {Mining graph data is an active research area. Several data mining methods and algorithms have been proposed to identify structures from graphs; still, the evaluation of those results is lacking. Within the framework of statistical hypothesis testing, we focus in this paper on randomization techniques for unweighted undirected graphs. Randomization is an important approach to assess the statistical significance of data mining results. Given an input graph, our randomization method will sample data from the class of graphs that share certain structural properties with the input graph. Here we describe three alternative algorithms based on local edge swapping and Metropolis sampling. We test our framework with various graph data sets and mining algorithms for two applications, namely graph clustering and frequent subgraph mining.} }

%0 = article %A = Hanhijärvi, Sami and Garriga, Gemma and Puolamäki, Kai %D = 2009 %T = Randomization techniques for graphs %U = http://eprints.pascal-network.org/archive/00004486/

@inproceedings{conf/pkdd/MirowskiL09, author = {Mirowski, Piotr W. and LeCun, Yann}, title = {Dynamic Factor Graphs for Time Series Modeling.}, editor = {Buntine, Wray L. and Grobelnik, Marko and Mladenic, Dunja and Shawe-Taylor, John}, booktitle = {ECML/PKDD (2)}, series = {Lecture Notes in Computer Science}, publisher = {Springer}, year = {2009}, volume = {5782}, pages = {128-143}, url = {http://dblp.uni-trier.de/db/conf/pkdd/pkdd2009-2.html#MirowskiL09}, isbn = {978-3-642-04173-0}, keywords = {2009, ecml, factor, graphs, pkdd, series, time} }

%0 = inproceedings %A = Mirowski, Piotr W. and LeCun, Yann %B = ECML/PKDD (2) %D = 2009 %I = Springer %T = Dynamic Factor Graphs for Time Series Modeling. %U = http://dblp.uni-trier.de/db/conf/pkdd/pkdd2009-2.html#MirowskiL09

@inproceedings{zhu2008graph, author = {Zhu, Feida and Chen, Chen and Yan, Xifeng and Han, Jiawei and Yu, Philip S}, title = {Graph OLAP: Towards Online Analytical Processing on Graphs}, booktitle = {Proc. 2008 Int. Conf. on Data Mining (ICDM'08), Pisa, Italy, Dec. 2008.}, year = {2008}, keywords = {graph, graphs, olap, sna} }

%0 = inproceedings %A = Zhu, Feida and Chen, Chen and Yan, Xifeng and Han, Jiawei and Yu, Philip S %B = Proc. 2008 Int. Conf. on Data Mining (ICDM'08), Pisa, Italy, Dec. 2008. %D = 2008 %T = Graph OLAP: Towards Online Analytical Processing on Graphs

Server logs of search engines store traces of queries submitted by users, which include queries themselves along with Webpages selected in their answers. Here we describe several graph-based relations among queries and many applications wherethese graphs could be used.

@article{baezayates2007graphs, author = {Baeza-Yates, Ricardo}, title = {Graphs from Search Engine Queries}, journal = {SOFSEM 2007: Theory and Practice of Computer Science}, year = {2007}, volume = {4362}, pages = {1--8}, url = {http://dx.doi.org/10.1007/978-3-540-69507-3_1}, keywords = {sofsem2007, baeza_yates, query_log_mining, graphs}, abstract = {Server logs of search engines store traces of queries submitted by users, which include queries themselves along with Webpages selected in their answers. Here we describe several graph-based relations among queries and many applications wherethese graphs could be used.} }

%0 = article %A = Baeza-Yates, Ricardo %D = 2007 %T = Graphs from Search Engine Queries %U = http://dx.doi.org/10.1007/978-3-540-69507-3_1

@proceedings{conf/iccs/2005,, title = {Conceptual Structures: Common Semantics for Sharing Knowledge, 13th International Conference on Conceptual Structures, ICCS 2005, Kassel, Germany, July 17-22, 2005, Proceedings}, editor = {Dau, Frithjof and Mugnier, Marie-Laure and Stumme, Gerd}, booktitle = {ICCS}, series = {Lecture Notes in Computer Science}, publisher = {Springer}, year = {2005}, volume = {3596}, url = {http://www.kde.cs.uni-kassel.de/conf/iccs05}, isbn = {3-540-27783-8}, keywords = {2005, Germany, Kassel, analysis, concept, conceptual, conference, fca, formal, graphs, iccs, knowledge, l3s, myown, proceedings, sharing, structures} }

%0 = proceedings %B = ICCS} %C = %D = 2005 %I = Springer %T = Conceptual Structures: Common Semantics for Sharing Knowledge, 13th International Conference on Conceptual Structures, ICCS 2005, Kassel, Germany, July 17-22, 2005, Proceedings} %U = http://www.kde.cs.uni-kassel.de/conf/iccs05

@proceedings{dau05contributions,, title = {Contributions to ICCS 2005}, editor = {Dau, Frithjof and Mugnier, Marie-Laure and Stumme, Gerd}, booktitle = {Contributions to ICCS 2005}, publisher = {kassel university press}, address = {Kassel}, year = {2005}, url = {http://www.kde.cs.uni-kassel.de/conf/iccs05}, isbn = {3-89958-138-5}, keywords = {2005, Germany, Kassel, analysis, concept, conceptual, conference, fca, formal, graphs, iccs, knowledge, l3s, myown, proceedings, sharing, structures} }

%0 = proceedings %B = Contributions to ICCS 2005} %C = Kassel %D = 2005 %I = kassel university press %T = Contributions to ICCS 2005} %U = http://www.kde.cs.uni-kassel.de/conf/iccs05

We introduce a concept of similarity between vertices of directed graphs. Let GA and GB be two directed graphs with, respectively, nA and nB vertices. We define an nB times nA similarity matrix S whose real entry sij expresses how similar vertex j (in GA) is to vertex i (in GB): we say that sij is their similarity score. The similarity matrix can be obtained as the limit of the normalized even iterates of Sk+1 = BSkAT + BTSkA, where A and B are adjacency matrices of the graphs and S0 is a matrix whose entries are all equal to 1. In the special case where GA = GB = G, the matrix S is square and the score sij is the similarity score between the vertices i and j of G. We point out that Kleinberg's "hub and authority" method to identify web-pages relevant to a given query can be viewed as a special case of our definition in the case where one of the graphs has two vertices and a unique directed edge between them. In analogy to Kleinberg, we show that our similarity scores are given by the components of a dominant eigenvector of a nonnegative matrix. Potential applications of our similarity concept are numerous. We illustrate an application for the automatic extraction of synonyms in a monolingual dictionary.

@article{blondel2004measure, author = {Blondel, Vincent D. and Gajardo, Anah and Heymans, Maureen and Senellart, Pierre and Dooren, Paul Van}, title = {A Measure of Similarity between Graph Vertices: Applications to Synonym Extraction and Web Searching}, journal = {SIAM Rev.}, publisher = {Society for Industrial and Applied Mathematics}, address = {Philadelphia, PA, USA}, year = {2004}, volume = {46}, number = {4}, pages = {647--666}, url = {http://portal.acm.org/citation.cfm?id=1035533.1035557}, doi = {http://dx.doi.org/10.1137/S0036144502415960}, issn = {0036-1445}, keywords = {detect, graphs, similarity, synonymy}, abstract = {We introduce a concept of similarity between vertices of directed graphs. Let GA and GB be two directed graphs with, respectively, nA and nB vertices. We define an nB times nA similarity matrix S whose real entry sij expresses how similar vertex j (in GA) is to vertex i (in GB): we say that sij is their similarity score. The similarity matrix can be obtained as the limit of the normalized even iterates of Sk+1 = BSkAT + BTSkA, where A and B are adjacency matrices of the graphs and S0 is a matrix whose entries are all equal to 1. In the special case where GA = GB = G, the matrix S is square and the score sij is the similarity score between the vertices i and j of G. We point out that Kleinberg's "hub and authority" method to identify web-pages relevant to a given query can be viewed as a special case of our definition in the case where one of the graphs has two vertices and a unique directed edge between them. In analogy to Kleinberg, we show that our similarity scores are given by the components of a dominant eigenvector of a nonnegative matrix. Potential applications of our similarity concept are numerous. We illustrate an application for the automatic extraction of synonyms in a monolingual dictionary.} }

%0 = article %A = Blondel, Vincent D. and Gajardo, Anah and Heymans, Maureen and Senellart, Pierre and Dooren, Paul Van %C = Philadelphia, PA, USA %D = 2004 %I = Society for Industrial and Applied Mathematics %T = A Measure of Similarity between Graph Vertices: Applications to Synonym Extraction and Web Searching %U = http://portal.acm.org/citation.cfm?id=1035533.1035557

@article{PhysRevE.70.056131, author = {Newman, M. E. J.}, title = {Analysis of weighted networks}, journal = {Phys. Rev. E}, publisher = {American Physical Society}, year = {2004}, volume = {70}, number = {5}, pages = {056131}, url = {http://pre.aps.org/abstract/PRE/v70/i5/e056131}, doi = {10.1103/PhysRevE.70.056131}, keywords = {COMMUNE, community, detection, graphs, modularity, networks, weighted} }

%0 = article %A = Newman, M. E. J. %D = 2004 %I = American Physical Society %T = Analysis of weighted networks %U = http://pre.aps.org/abstract/PRE/v70/i5/e056131

@proceedings{delugach01conceptual,, title = {Conceptual Structures -- Broadening the Base. Proc. 9th International Conference on Conceptual Structures}, editor = {Delugach, H. and Stumme, G.}, series = {LNAI}, publisher = {Springer}, address = {Heidelberg}, year = {2001}, volume = {2120}, keywords = {2001, analysis, cg, cgs, concept, conceptual, fca, formal, graphs, iccs, myown, structures} }

%0 = proceedings %B = } %C = Heidelberg %D = 2001 %I = Springer %T = Conceptual Structures -- Broadening the Base. Proc. 9th International Conference on Conceptual Structures} %U =

@inproceedings{eklund00contextual, author = {Eklund, P. and Groh, B. and Stumme, G. and Wille, R.}, title = {Contextual-Logic Extension of TOSCANA.}, editor = {Ganter, B. and Mineau, G. W.}, booktitle = {Conceptual Structures: Logical, Linguistic, and Computational}, series = {LNAI}, publisher = {Springer}, address = {Heidelberg}, year = {2000}, volume = {1867}, pages = {453-467}, url = {http://www.kde.cs.uni-kassel.de/stumme/papers/2000/ICCS_toscanaextension.pdf}, keywords = {2000, analysis, cg, cgs, concept, conceptual, fca, formal, graph, graphs, iccs, myown, toscana} }

%0 = inproceedings %A = Eklund, P. and Groh, B. and Stumme, G. and Wille, R. %B = Conceptual Structures: Logical, Linguistic, and Computational %C = Heidelberg %D = 2000 %I = Springer %T = Contextual-Logic Extension of TOSCANA. %U = http://www.kde.cs.uni-kassel.de/stumme/papers/2000/ICCS_toscanaextension.pdf

@article{stumme008thinternational, author = {Stumme, G.}, title = {8th International Conference on Conceptual Structures. Conference Report}, journal = {Knowledge Organization}, year = {2000}, volume = {27}, number = {3}, pages = {162}, url = {http://www.kde.cs.uni-kassel.de/stumme/papers/2000/ConferenceReportICCS00.pdf}, keywords = {2000, analysis, cg, concept, conceptual, conference, fcacgs, formal, graphs, iccs, lattices, myown, report, structures} }

%0 = article %A = Stumme, G. %D = 2000 %T = 8th International Conference on Conceptual Structures. Conference Report %U = http://www.kde.cs.uni-kassel.de/stumme/papers/2000/ConferenceReportICCS00.pdf

@proceedings{stumme00working,, title = {Working with Conceptual Structures -- Contributions to ICCS 2000. Suppl. Proc. 8th International
Conference on Conceptual Structures (ICCS 2000)}, editor = {Stumme, G.}, publisher = {Shaker}, address = {Aachen}, year = {2000}, keywords = {2000, analysis, cg, cgs, concept, conceptual, conference, fca, formal, graphs, iccs, myown, proceedings, structures} }

%0 = proceedings %B = } %C = Aachen %D = 2000 %I = Shaker %T = Working with Conceptual Structures -- Contributions to ICCS 2000. Suppl. Proc. 8th International
Conference on Conceptual Structures (ICCS 2000)} %U =

@inproceedings{mineau99conceptual, author = {Mineau, Guy and Stumme, Gerd and Wille, Rudolf}, title = {Conceptual Structures Represented by Conceptual Graphs and Formal Concept Analysis}, editor = {Tepfenhart, W. and Cyre, W.}, booktitle = {Conceptual Structures: Standards and Practices. Proc. ICCS '99}, series = {LNAI}, publisher = {Springer}, address = {Heidelberg}, year = {1999}, volume = {1640}, pages = {423-441}, url = {http://www.kde.cs.uni-kassel.de/stumme/papers/1999/ICCS99.pdf}, keywords = {1999, analysis, cg, cgs, concept, conceptual, fca, formal, graphs, iccs, knowledge, myown, representation, structures} }

%0 = inproceedings %A = Mineau, Guy and Stumme, Gerd and Wille, Rudolf %B = Conceptual Structures: Standards and Practices. Proc. ICCS '99 %C = Heidelberg %D = 1999 %I = Springer %T = Conceptual Structures Represented by Conceptual Graphs and Formal Concept Analysis %U = http://www.kde.cs.uni-kassel.de/stumme/papers/1999/ICCS99.pdf

@inproceedings{wille97conceptual, author = {Wille, Rudolf}, title = {Conceptual Graphs and Formal Concept Analysis}, editor = {Lukose, D. and Delugach, H. and Keeler, M. and Searle, L. and Sowa, J. F.}, booktitle = {Conceptual Structures: Fulfilling Peirce's Dream}, series = {Lecture Notes in Artificial Intelligence}, publisher = {Springer}, address = {Heidelberg}, year = {1997}, volume = {1257}, pages = {290--303}, keywords = {ag1, analysis, begriffsanalyse, cg, concept, conceptual, darmstadt, fba, fca, formal, graph, graphs} }

%0 = inproceedings %A = Wille, Rudolf %B = Conceptual Structures: Fulfilling Peirce's Dream %C = Heidelberg %D = 1997 %I = Springer %T = Conceptual Graphs and Formal Concept Analysis

Nous définissons précisément les notions de base du modèle des graphes conceptuels de Sowa [Sowa 84] et en étudions les propriétés. Nos résultats portent principalement sur la structure de la relation de spécialisation, la correspondance entre opérations de graphes et opérations logiques, et la complexité algorithmique de la mise en œuvre du modèle

@article{m1992conceptual, author = {Chein, Michel and Mugnier, Marie-Laure}, title = {Conceptual graphs: fundamental notions}, series = {4}, journal = {Revue d'Intelligence Artificielle}, address = {Lavoisier}, year = {1992}, volume = {6}, pages = {365-406}, keywords = {conceptual, fundamental, graphs, notions}, abstract = {Nous définissons précisément les notions de base du modèle des graphes conceptuels de Sowa [Sowa 84] et en étudions les propriétés. Nos résultats portent principalement sur la structure de la relation de spécialisation, la correspondance entre opérations de graphes et opérations logiques, et la complexité algorithmique de la mise en œuvre du modèle } }

%0 = article %A = Chein, Michel and Mugnier, Marie-Laure %C = Lavoisier %D = 1992 %T = Conceptual graphs: fundamental notions

@book{sowa84, author = {Sowa, J. F.}, title = {Conceptual Structures: Information Processing in Mind and Machine}, publisher = {Addison-Wesley Publishing Company}, address = {Reading, MA}, year = {1984}, keywords = {cg, cgs, conceptual, graphs, information, structures} }

%0 = book %A = Sowa, J. F. %C = Reading, MA %D = 1984 %I = Addison-Wesley Publishing Company %T = Conceptual Structures: Information Processing in Mind and Machine

@article{erdos1959, author = {Erdős, Pal and Rényi, Alfréd}, title = {On Random Graphs}, journal = {Publications Mathematicae}, year = {1959}, volume = {6}, pages = {290}, keywords = {analysis, graphs, network, random} }

%0 = article %A = Erdős, Pal and Rényi, Alfréd %D = 1959 %T = On Random Graphs