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88
Comparing community structure identification
 Journal of Statistical Mechanics: Theory and Experiment
, 2005
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Graph Clustering Based on Structural/Attribute Similarities
"... The goal of graph clustering is to partition vertices in a large graph into different clusters based on various criteria such as vertex connectivity or neighborhood similarity. Graph clustering techniques are very useful for detecting densely connected groups in a large graph. Many existing graph cl ..."
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Cited by 42 (2 self)
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The goal of graph clustering is to partition vertices in a large graph into different clusters based on various criteria such as vertex connectivity or neighborhood similarity. Graph clustering techniques are very useful for detecting densely connected groups in a large graph. Many existing graph clustering methods mainly focus on the topological structure for clustering, but largely ignore the vertex properties which are often heterogenous. In this paper, we propose a novel graph clustering algorithm, SACluster, based on both structural and attribute similarities through a unified distance measure. Our method partitions a large graph associated with attributes into k clusters so that each cluster contains a densely connected subgraph with homogeneous attribute values. An effective method is proposed to automatically learn the degree of contributions of structural similarity and attribute similarity. Theoretical analysis is provided to show that SACluster is converging. Extensive experimental results demonstrate the effectiveness of SACluster through comparison with the stateoftheart graph clustering and summarization methods. 1.
An Emulator Network for
 SIMD Machine Interconnection Networks, in: Proc. 6 th annual symposium on Computer architecture
, 1979
"... Fig. 0.1. [Proposed cover figure.] The largest connected component of a network of network scientists. This network was constructed based on the coauthorship of papers listed in two wellknown review articles [13,83] and a small number of additional papers that were added manually [86]. Each node is ..."
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Cited by 36 (3 self)
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Fig. 0.1. [Proposed cover figure.] The largest connected component of a network of network scientists. This network was constructed based on the coauthorship of papers listed in two wellknown review articles [13,83] and a small number of additional papers that were added manually [86]. Each node is colored according to community membership, which was determined using a leadingeigenvector spectral method followed by KernighanLin nodeswapping steps [64, 86, 107]. To determine community placement, we used the FruchtermanReingold graph visualization [45], a forcedirected layout method that is related to maximizing a quality function known as modularity [92]. To apply this method, we treated the communities as if they were themselves the nodes of a (significantly smaller) network with connections rescaled by intercommunity links. We then used the KamadaKawaii springembedding graph visualization algorithm [62] to place the nodes of each individual community (ignoring intercommunity links) and then to rotate and flip the communities for optimal placement (including intercommunity links). We gratefully acknowledge Amanda Traud for preparing this figure. COMMUNITIES IN NETWORKS
Multilevel algorithms for modularity clustering
"... been adapted to modularity clustering. Section 4 details the singlelevel and multilevel refinement heuristics, and Section 5.3 compares them experimentally. Because the effectiveness of (particularly multilevel) refinement may depend on the coarsening algorithm, Section 5.4 examines various combi ..."
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Cited by 25 (0 self)
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been adapted to modularity clustering. Section 4 details the singlelevel and multilevel refinement heuristics, and Section 5.3 compares them experimentally. Because the effectiveness of (particularly multilevel) refinement may depend on the coarsening algorithm, Section 5.4 examines various combinations of coarsening and refinement heuristics. Section 6 compares public implementations and benchmark results of modularity clustering heuristics, without a restriction to coarsening and refinement algorithms. While this is one of the most extensive comparisons in the literature, it is far from exhaustive, because implementations and sufficient experimental results have not been published for some proposed heurisarXiv:0812.4073v1
An experimental investigation of graph kernels on a collaborative recommendation task
 Proceedings of the 6th International Conference on Data Mining (ICDM 2006
, 2006
"... This paper presents a survey as well as a systematic empirical comparison of seven graph kernels and two related similarity matrices (simply referred to as graph kernels), namely the exponential diffusion kernel, the Laplacian exponential diffusion kernel, the von Neumann diffusion kernel, the regul ..."
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Cited by 19 (6 self)
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This paper presents a survey as well as a systematic empirical comparison of seven graph kernels and two related similarity matrices (simply referred to as graph kernels), namely the exponential diffusion kernel, the Laplacian exponential diffusion kernel, the von Neumann diffusion kernel, the regularized Laplacian kernel, the commutetime kernel, the randomwalkwithrestart similarity matrix, and finally, three graph kernels introduced in this paper: the regularized commutetime kernel, the Markov diffusion kernel, and the crossentropy diffusion matrix. The kernelonagraph approach is simple and intuitive. It is illustrated by applying the nine graph kernels to a collaborativerecommendation task and to a semisupervised classification task, both on several databases. The graph methods compute proximity measures between nodes that help study the structure of the graph. Our comparisons suggest that the regularized commutetime and the Markov diffusion kernels perform best, closely followed by the regularized Laplacian kernel. 1
A fast algorithm to find overlapping communities in networks
 In Proc. of ECML/PKDD 2008
, 2008
"... Abstract. Many networks possess a community structure, such that vertices form densely connected groups which are more sparsely linked to other groups. In some cases these groups overlap, with some vertices shared between two or more communities. Discovering communities in networks is a computationa ..."
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Cited by 15 (1 self)
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Abstract. Many networks possess a community structure, such that vertices form densely connected groups which are more sparsely linked to other groups. In some cases these groups overlap, with some vertices shared between two or more communities. Discovering communities in networks is a computationally challenging task, especially if they overlap. In previous work we proposed an algorithm, CONGA, that could detect overlapping communities using the new concept of split betweenness. Here we present an improved algorithm based on a local form of betweenness, which yields good results but is much faster. It is especially effective in discovering smalldiameter communities in large networks, and has a time complexity of only O(n log n) for sparse networks. 1 Introduction and Related Work In recent years, networks (graphs) have increasingly been used to represent various kinds of complex system in the real world. Many networks exhibit community structure: the tendency of vertices to form communities (or modules) such that intracommunity edges are denser than the edges between communities. Communities often
A family of dissimilarity measures between nodes generalizing both the shortestpath and the commutetime distances
 in Proceedings of the 14th SIGKDD International Conference on Knowledge Discovery and Data Mining
"... This work introduces a new family of linkbased dissimilarity measures between nodes of a weighted directed graph. This measure, called the randomized shortestpath (RSP) dissimilarity, depends on a parameter θ and has the interesting property of reducing, on one end, to the standard shortestpath d ..."
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Cited by 14 (7 self)
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This work introduces a new family of linkbased dissimilarity measures between nodes of a weighted directed graph. This measure, called the randomized shortestpath (RSP) dissimilarity, depends on a parameter θ and has the interesting property of reducing, on one end, to the standard shortestpath distance when θ is large and, on the other end, to the commutetime (or resistance) distance when θ is small (near zero). Intuitively, it corresponds to the expected cost incurred by a random walker in order to reach a destination node from a starting node while maintaining a constant entropy (related to θ) spread in the graph. The parameter θ is therefore biasing gradually the simple random walk on the graph towards the shortestpath policy. By adopting a statistical physics approach and computing a sum over all the possible paths (discrete path integral), it is shown that the RSP dissimilarity from every node to a particular node of interest can be computed efficiently by solving two linear systems of n equations, where n is the number of nodes. On the other hand, the dissimilarity between every couple of nodes is obtained by inverting an n × n matrix. The proposed measure can be used for various graph mining tasks such as computing betweenness centrality, finding dense communities, etc, as shown in the experimental section.
Graph nodes clustering with the sigmoid commutetime kernel: A . . .
 DATA & KNOWLEDGE ENGINEERING
, 2009
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Laplacian dynamics and multiscale modular structure in networks
 ArXiv
, 2009
"... Most methods proposed to uncover communities in complex networks rely on their structural properties. Here we introduce the stability of a network partition, a measure of its quality defined in terms of the statistical properties of a dynamical process taking place on the graph. The timescale of th ..."
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Cited by 10 (1 self)
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Most methods proposed to uncover communities in complex networks rely on their structural properties. Here we introduce the stability of a network partition, a measure of its quality defined in terms of the statistical properties of a dynamical process taking place on the graph. The timescale of the process acts as an intrinsic parameter that uncovers community structures at different resolutions. The stability extends and unifies standard notions for community detection: modularity and spectral partitioning can be seen as limiting cases of our dynamic measure. Similarly, recently proposed multiresolution methods correspond to linearisations of the stability at short times. The connection between community detection and Laplacian dynamics enables us to establish dynamically motivated stability measures linked to distinct null models. We apply our method to find multiscale partitions for different networks and show that the stability can be computed efficiently for large networks with extended versions of current algorithms. The relation between the structure of a network and the dynamics that takes place on it 1 Lambiotte et al. has been studied extensively in the last years 1,2,3. A growing body of research has shown how
Community detection using a neighborhood strength driven label propagation algorithm
 IN: IEEE NSW
, 2011
"... Studies of community structure and evolution in large social networks require a fast and accurate algorithm for community detection. As the size of analyzed communities grows, complexity of the community detection algorithm needs to be kept close to linear. The Label Propagation Algorithm (LPA) has ..."
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Cited by 9 (6 self)
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Studies of community structure and evolution in large social networks require a fast and accurate algorithm for community detection. As the size of analyzed communities grows, complexity of the community detection algorithm needs to be kept close to linear. The Label Propagation Algorithm (LPA) has the benefits of nearlylinear running time and easy implementation, thus it forms a good basis for efficient community detection methods. In this paper, we propose new update rule and label propagation criterion in LPA to improve both its computational efficiency and the quality of communities that it detects. The speed is optimized by avoiding unnecessary updates performed by the original algorithm. This change reduces significantly (by order of magnitude for large networks) the number of iterations that the algorithm executes. We also evaluate our generalization of the LPA update rule that takes into account, with varying strength, connections to the neighborhood of a node considering a new label. Experiments on computer generated networks and a wide range of social networks show that our new rule improves the quality of the detected communities compared to those found by the original LPA. The benefit of considering positive neighborhood strength is pronounced especially on realworld networks containing sufficiently large fraction of nodes with high clustering coefficient.