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WinnerTakeAll Networks
 Part III: Articles
"... clustering via clique relaxations: A community based approach ..."
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clustering via clique relaxations: A community based approach
A Classification for Community Discovery Methods in Complex Networks
, 2011
"... Many realworld networks are intimately organized according to a community structure. Much research effort has been devoted to develop methods and algorithms that can efficiently highlight this hidden structure of a network, yielding a vast literature on what is called today community detection. S ..."
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Many realworld networks are intimately organized according to a community structure. Much research effort has been devoted to develop methods and algorithms that can efficiently highlight this hidden structure of a network, yielding a vast literature on what is called today community detection. Since network representation can be very complex and can contain different variants in the traditional graph model, each algorithm in the literature focuses on some of these properties and establishes, explicitly or implicitly, its own definition of community. According to this definition, each proposed algorithm then extracts the communities, which typically reflect only part of the features of real communities. The aim of this survey is to provide a ‘user manual’ for the community discovery problem. Given a meta definition of what a community in a social network is, our aim is to organize the main categories of community discovery methods based on the definition of community they adopt. Given a desired definition of community and the features of a problem (size of network, direction of edges, multidimensionality, and so on) this review paper is designed to provide a set of approaches that researchers could focus on. The proposed classification of community discovery methods is also useful for putting into perspective the many open
A more relaxed model for graphbased data clustering: splex editing
 In Proc. 5th AAIM, LNCS
, 2009
"... Abstract. We introduce the sPlex Editing problem generalizing the wellstudied Cluster Editing problem, both being NPhard and both being motivated by graphbased data clustering. Instead of transforming a given graph by a minimum number of edge modifications into a disjoint union of cliques (Clust ..."
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Abstract. We introduce the sPlex Editing problem generalizing the wellstudied Cluster Editing problem, both being NPhard and both being motivated by graphbased data clustering. Instead of transforming a given graph by a minimum number of edge modifications into a disjoint union of cliques (Cluster Editing), the task in the case of sPlex Editing is now to transform a graph into a disjoint union of socalled splexes. Herein, an splex denotes a vertex set inducing a (sub)graph where every vertex has edges to all but at most s vertices in the splex. Cliques are 1plexes. The advantage of splexes for s ≥ 2 is that they allow to model a more relaxed cluster notion (splexes instead of cliques), which better reflects inaccuracies of the input data. We develop a provably efficient and effective preprocessing based on data reduction (yielding a socalled problem kernel), a forbidden subgraph characterization of splex cluster graphs, and a depthbounded search tree which is used to find optimal edge modification sets. Altogether, this yields efficient algorithms in case of moderate numbers of edge modifications. 1
Various isolation concepts for the enumeration of dense subgraphs
 Diplomarbeit, Institut für Informatik, FriedrichSchiller Universität Jena
"... Abstract. In a graph G = (V, E), a vertex subset S ⊆ V of size k is called cisolated if it has less than c · k outgoing edges. We repair a nontrivially flawed algorithm for enumerating all cisolated cliques due to Ito et al. [European Symposium on Algorithms 2005] and obtain an algorithm running i ..."
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Abstract. In a graph G = (V, E), a vertex subset S ⊆ V of size k is called cisolated if it has less than c · k outgoing edges. We repair a nontrivially flawed algorithm for enumerating all cisolated cliques due to Ito et al. [European Symposium on Algorithms 2005] and obtain an algorithm running in O(4 c · c 4 · E) time. We describe a speedup trick that also helps parallelizing the enumeration. Moreover, we introduce a more restricted and a more general isolation concept and show that both lead to faster enumeration algorithms. Finally, we extend our considerations to splexes (a relaxation of the clique notion), pointing out a W[1]hardness result and providing a fixedparameter algorithm for enumerating isolated splexes. 1
A GENERALIZATION OF NEMHAUSER AND TROTTER’S LOCAL OPTIMIZATION THEOREM
, 2009
"... The NemhauserTrotter local optimization theorem applies to the NPhard Vertex Cover problem and has applications in approximation as well as parameterized algorithmics. We present a framework that generalizes Nemhauser and Trotter’s result to vertex deletion and graph packing problems, introducin ..."
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The NemhauserTrotter local optimization theorem applies to the NPhard Vertex Cover problem and has applications in approximation as well as parameterized algorithmics. We present a framework that generalizes Nemhauser and Trotter’s result to vertex deletion and graph packing problems, introducing novel algorithmic strategies based on purely combinatorial arguments (not referring to linear programming as the NemhauserTrotter result originally did). We exhibit our framework using a generalization of Vertex Cover, called BoundedDegree Deletion, that has promise to become an important tool in the analysis of gene and other biological networks. For some fixed d ≥ 0, BoundedDegree Deletion asks to delete as few vertices as possible from a graph in order to transform it into a graph with maximum vertex degree at most d. Vertex Cover is the special case of d = 0. Our generalization of the NemhauserTrotter theorem implies that BoundedDegree Deletion has a problem kernel with a linear number of vertices for every constant d. We also outline an application of our extremal combinatorial approach to the problem of packing stars with a bounded number of leaves. Finally, charting the border between (parameterized) tractability and intractability for BoundedDegree Deletion, we provide a W[2]hardness result for BoundedDegree Deletion in case of unbounded dvalues.
Streaming Algorithms for kcore Decomposition
"... A kcore of a graph is a maximal connected subgraph in which every vertex is connected to at least k vertices in the subgraph. kcore decomposition is often used in largescale network analysis, such as community detection, protein function prediction, visualization, and solving NPHard problems on ..."
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A kcore of a graph is a maximal connected subgraph in which every vertex is connected to at least k vertices in the subgraph. kcore decomposition is often used in largescale network analysis, such as community detection, protein function prediction, visualization, and solving NPHard problems on real networks efficiently, like maximal clique finding. In many realworld applications, networks change over time. As a result, it is essential to develop efficient incremental algorithms for streaming graph data. In this paper, we propose the first incremental kcore decomposition algorithms for streaming graph data. These algorithms locate a small subgraph that is guaranteed to contain the list of vertices whose maximum kcore values have to be updated, and efficiently process this subgraph to update the kcore decomposition. Our results show a significant reduction in runtime compared to nonincremental alternatives. We show the efficiency of our algorithms on different types of real and synthetic graphs, at different scales. For a graph of 16 million vertices, we observe speedups reaching a million times, relative to the nonincremental algorithms. 1.
Algorithms and experiments for clique relaxations—finding maximum splexes
 In Proceedings of the 8th International Symposium on Experimental Algorithms (SEA ’09), volume 5526 of LNCS
, 2009
"... Abstract. We propose new practical algorithms to find degreerelaxed variants of cliques called splexes. An splex denotes a vertex subset in a graph inducing a subgraph where every vertex has edges to all but at most s vertices in the splex. Cliques are 1plexes. In analogy to the special case of ..."
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Abstract. We propose new practical algorithms to find degreerelaxed variants of cliques called splexes. An splex denotes a vertex subset in a graph inducing a subgraph where every vertex has edges to all but at most s vertices in the splex. Cliques are 1plexes. In analogy to the special case of finding maximumcardinality cliques, finding maximumcardinality splexes is NPhard. Complementing previous work, we develop combinatorial, exact algorithms, which are strongly based on methods from parameterized algorithmics. The experiments with our freely available implementation indicate the competitiveness of our approach, for many realworld graphs outperforming the previously used methods. 1
Isolation Concepts for Efficiently Enumerating Dense Subgraphs
, 2009
"... In an undirected graph G = (V,E), a set of k vertices is called cisolated if it has less than c · k outgoing edges. Ito and Iwama [ACM Trans. Algorithms, to appear] gave an algorithm to enumerate all cisolated maximal cliques in O(4 c ·c 4 · E) time. We extend this to enumerating all maximal ci ..."
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In an undirected graph G = (V,E), a set of k vertices is called cisolated if it has less than c · k outgoing edges. Ito and Iwama [ACM Trans. Algorithms, to appear] gave an algorithm to enumerate all cisolated maximal cliques in O(4 c ·c 4 · E) time. We extend this to enumerating all maximal cisolated cliques (which are a superset) and improve the running time bound to O(2.89 c ·c 2 ·E), using modifications which also facilitate parallelizing the enumeration. Moreover, we introduce a more restricted and a more general isolation concept and show that both lead to faster enumeration algorithms. Finally, we extend our considerations to splexes (a relaxation of the clique notion), providing a W[1]hardness result when the size of the splex is the parameter and a fixedparameter algorithm for enumerating isolated splexes when the parameter describes the degree of isolation.
Combinatorial algorithms for the maximum kplex problem
, 2009
"... The maximum clique problem provides a classic framework for detecting cohesive subgraphs. However, this approach can fail to detect much of the cohesive structure in a graph. To address this issue, Seidman and Foster introduced kplexes as a degreebased relaxation of graph completeness. More recen ..."
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The maximum clique problem provides a classic framework for detecting cohesive subgraphs. However, this approach can fail to detect much of the cohesive structure in a graph. To address this issue, Seidman and Foster introduced kplexes as a degreebased relaxation of graph completeness. More recently, Balasundaram et al. formulated the maximum kplex problem as an integer program and designed a branchandcut algorithm. This paper derives a new upper bound on the cardinality of kplexes and adapts combinatorial clique algorithms to find maximum kplexes. 1.
Keywords Learning and Inference in Massive Social Networks
"... Researchers and practitioners increasingly are gaining access to data on explicit social networks. For example, telecommunications and technology firms record data on consumer networks (via phone calls, emails, voiceoverIP, instant messaging), ..."
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Researchers and practitioners increasingly are gaining access to data on explicit social networks. For example, telecommunications and technology firms record data on consumer networks (via phone calls, emails, voiceoverIP, instant messaging),