Heidtmann, K. (2013), 'Internet-Graphen', Informatik-Spektrum 36 (5) , 440-448 .
[BibTeX] [Endnote]

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.

Mucha, P. J.; Richardson, T.; Macon, K.; Porter, M. A. & Onnela, J.-P. (2010), 'Community Structure in Time-Dependent, Multiscale, and Multiplex Networks', Science 328 (5980) , 876-878 .
[BibTeX] [Endnote]

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.

2009

Ghosh, R. & Lerman, K. (2009), 'Structure of Heterogeneous Networks' , cite arxiv:0906.2212 .
[BibTeX] [Endnote]

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.

Hanhijärvi, S.; Garriga, G. & Puolamäki, K. (2009), 'Randomization techniques for graphs', .
[BibTeX] [Endnote]

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.

Mirowski, P. W. & LeCun, Y. (2009), Dynamic Factor Graphs for Time Series Modeling., in Wray L. Buntine; Marko Grobelnik; Dunja Mladenic & John Shawe-Taylor, ed., 'ECML/PKDD (2)' , Springer, , pp. 128-143 .
[BibTeX] [Endnote]

2008

Zhu, F.; Chen, C.; Yan, X.; Han, J. & Yu, P. S. (2008), Graph OLAP: Towards Online Analytical Processing on Graphs, in 'Proc. 2008 Int. Conf. on Data Mining (ICDM'08), Pisa, Italy, Dec. 2008.' .
[BibTeX] [Endnote]

2007

Baeza-Yates, R. (2007), 'Graphs from Search Engine Queries', SOFSEM 2007: Theory and Practice of Computer Science 4362 , 1--8 .
[BibTeX] [Endnote]

2005

Dau, F.; Mugnier, M.-L. & Stumme, G., ed. (2005), Conceptual Structures: Common Semantics for Sharing Knowledge, 13th International Conference on Conceptual Structures, ICCS 2005, Kassel, Germany, July 17-22, 2005, Proceedings , Vol. 3596 , Springer .
[BibTeX] [Endnote]

Dau, F.; Mugnier, M.-L. & Stumme, G., ed. (2005), Contributions to ICCS 2005 , kassel university press , Kassel .
[BibTeX] [Endnote]

2004

Blondel, V. D.; Gajardo, A.; Heymans, M.; Senellart, P. & Dooren, P. V. (2004), 'A Measure of Similarity between Graph Vertices: Applications to Synonym Extraction and Web Searching', SIAM Rev. 46 (4) , 647--666 .
[BibTeX] [Endnote]

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.

Newman, M. E. J. (2004), 'Analysis of weighted networks', Phys. Rev. E 70 (5) , 056131 .
[BibTeX] [Endnote]

2001

Delugach, H. & Stumme, G., ed. (2001), Conceptual Structures -- Broadening the Base. Proc. 9th International Conference on Conceptual Structures , Vol. 2120 , Springer , Heidelberg .
[BibTeX] [Endnote]

2000

Eklund, P.; Groh, B.; Stumme, G. & Wille, R. (2000), Contextual-Logic Extension of TOSCANA., in B. Ganter & G. W. Mineau, ed., 'Conceptual Structures: Logical, Linguistic, and Computational' , Springer, Heidelberg , pp. 453-467 .
[BibTeX] [Endnote]

Stumme, G. (2000), '8th International Conference on Conceptual Structures. Conference Report', Knowledge Organization 27 (3) , 162 .
[BibTeX] [Endnote]

Stumme, G., ed. (2000), Working with Conceptual Structures -- Contributions to ICCS 2000. Suppl. Proc. 8th International
Conference on Conceptual Structures (ICCS 2000) , Shaker , Aachen .
[BibTeX] [Endnote]

1999

Mineau, G.; Stumme, G. & Wille, R. (1999), Conceptual Structures Represented by Conceptual Graphs and Formal Concept Analysis, in W. Tepfenhart & W. Cyre, ed., 'Conceptual Structures: Standards and Practices. Proc. ICCS '99' , Springer, Heidelberg , pp. 423-441 .
[BibTeX] [Endnote]

1997

Wille, R. (1997), Conceptual Graphs and Formal Concept Analysis, in D. Lukose; H. Delugach; M. Keeler; L. Searle & J. F. Sowa, ed., 'Conceptual Structures: Fulfilling Peirce's Dream' , Springer, Heidelberg , pp. 290--303 .
[BibTeX] [Endnote]

1992

Chein, M. & Mugnier, M.-L. (1992), 'Conceptual graphs: fundamental notions', Revue d'Intelligence Artificielle 6 , 365-406 .
[BibTeX] [Endnote]

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

1984

Sowa, J. F. (1984), Conceptual Structures: Information Processing in Mind and Machine , Addison-Wesley Publishing Company , Reading, MA .
[BibTeX] [Endnote]

1959

Erdős, P. & Rényi, A. (1959), 'On Random Graphs', Publications Mathematicae 6 , 290 .
[BibTeX] [Endnote]