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Finding community structure in networks using the eigenvectors of matrices. Phys
 Rev. E
"... We consider the problem of detecting communities or modules in networks, groups of vertices with a higherthanaverage density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as “modularity ” over possible div ..."
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Cited by 223 (0 self)
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We consider the problem of detecting communities or modules in networks, groups of vertices with a higherthanaverage density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as “modularity ” over possible divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a new centrality measure that identifies those vertices that occupy central positions within the communities to which they belong. The algorithms and measures proposed are illustrated with applications to a variety of realworld complex networks. I.
Comparing community structure identification
 Journal of Statistical Mechanics: Theory and Experiment
, 2005
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Graph nodes clustering with the sigmoid commutetime kernel: A . . .
 DATA & KNOWLEDGE ENGINEERING
, 2009
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The sumoverpaths covariance kernel: A novel covariance measure between nodes of a directed graph
 the IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2009
"... Abstract—This work introduces a linkbased covariance measure between the nodes of a weighted directed graph where a cost is associated to each arc. To this end, a probability distribution on the (usually infinite) countable set of paths through the graph is defined by minimizing the total expected ..."
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Cited by 9 (7 self)
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Abstract—This work introduces a linkbased covariance measure between the nodes of a weighted directed graph where a cost is associated to each arc. To this end, a probability distribution on the (usually infinite) countable set of paths through the graph is defined by minimizing the total expected cost between all pairs of nodes while fixing the total relative entropy spread in the graph. This results in a Boltzmann distribution on the set of paths such that long (highcost) paths occur with a low probability while short (lowcost) paths occur with a high probability. The sumoverpaths (SoP) covariance measure between nodes is then defined according to this probability distribution: two nodes are considered as highly correlated if they often cooccur together on the same – preferably short – paths. The resulting covariance matrix between nodes (say n nodes in total) is a Gram matrix and therefore defines a valid kernel on the graph. It is obtained by inverting a n × n matrix depending on the costs assigned to the arcs. In the same spirit, a betweenness score is also defined, measuring the expected number of times a node occurs on a path. The proposed measures could be used for various graph mining tasks such as computing betweenness centrality, semisupervised classification of nodes, visualization, etc, as shown in the experimental section. Index Terms—Graph mining, kernel on a graph, shortest path, correlation measure, betweenness measure, resistance distance, commutetime distance, biased random walk, semisupervised classification.
Finding Community Structure Based on Subgraph Similarity
, 902
"... Abstract Community identification is a longstanding challenge in the modern network science, especially for very large scale networks containing millions of nodes. In this paper, we propose a new metric to quantify the structural similarity between subgraphs, based on which an algorithm for communi ..."
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Cited by 3 (0 self)
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Abstract Community identification is a longstanding challenge in the modern network science, especially for very large scale networks containing millions of nodes. In this paper, we propose a new metric to quantify the structural similarity between subgraphs, based on which an algorithm for community identification is designed. Extensive empirical results on several real networks from disparate fields has demonstrated that the present algorithm can provide the same level of reliability, measure by modularity, while takes much shorter time than the wellknown fast algorithm proposed by Clauset, Newman and Moore (CNM). We further propose a hybrid algorithm that can simultaneously enhance modularity and save computational time compared with the CNM algorithm. 1
Organization Detection using Emergent Computing
 Int. Transactions on Systems Science and Applications, Special Issue "SelfOrganizing, SelfManaging Computing and Communications
, 2006
"... Abstract: Organization is a central concept in systems. In this paper an ant algorithm for detecting organizations is presented. In a discretetime context, at each timestep, an organization corresponds to a set of closely interacting entities in a system. This system is mapped to a graph where nod ..."
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Cited by 2 (2 self)
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Abstract: Organization is a central concept in systems. In this paper an ant algorithm for detecting organizations is presented. In a discretetime context, at each timestep, an organization corresponds to a set of closely interacting entities in a system. This system is mapped to a graph where nodes represent entities and edges represent interrelations. Several colonies of ants compete, and inside each colony, ants collaborate in order to colonize the graph. Detected organizations emerge from the global behavior of the ants. The proposed approach is compared to other methods on a graph where the organizations are already known. It is then tested on two real world graphs studied in the related literature.
CLUSTERING METHODS IN PROTEINPROTEIN INTERACTION NETWORK
"... With completion of a draft sequence of the human genome, the field of genetics stands on the threshold of significant theoretical and practical advances. Crucial to furthering these investigations is a comprehensive understanding of the expression, function, and regulation of the proteins encoded by ..."
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With completion of a draft sequence of the human genome, the field of genetics stands on the threshold of significant theoretical and practical advances. Crucial to furthering these investigations is a comprehensive understanding of the expression, function, and regulation of the proteins encoded by an organism. It has been observed that proteins seldom act as single isolated species in the performance of their functions; rather, proteins involved in the same cellular processes often interact with each other. Therefore, the functions of uncharacterized proteins can be predicted through comparison with the interactions of similar known proteins. A detailed examination of the proteinprotein interaction (PPI) network can thus yield significant new understanding of protein function. Clustering is the process of grouping data objects into sets (clusters) which demonstrate greater similarity among objects in the same cluster than in different clusters. Clustering in the PPI network context groups together proteins which share a larger number of interactions. The results of this process can illuminate the structure of the PPI network and suggest possible functions for members of the cluster which were previously uncharacterized. This chapter will begin with a brief introduction of the properties of proteinprotein interaction networks, including a review of the data which has been generated by both experimental and computational approaches. A variety of methods which have been employed to cluster these networks will then be presented. These approaches are broadly characterized as either distancebased or
Predicting Recent Links in FOAF Networks
"... Abstract. For social networks, prediction of new links or edges can be important for many reasons, in particular for understanding future network growth. Recent work has shown that graph vertex similarity measures are good at predicting graph link formation for the near future, but are less effectiv ..."
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Abstract. For social networks, prediction of new links or edges can be important for many reasons, in particular for understanding future network growth. Recent work has shown that graph vertex similarity measures are good at predicting graph link formation for the near future, but are less effective in predicting further out. This could imply that recent links can be more important than older links in link prediction. To see if this is indeed the case, we apply a new relation strength similarity (RSS) measure on a coauthorship network constructed from a subset of the CiteSeer X dataset to study the power of recency. We choose RSS because it is one of the few similarity measures designed for weighted networks and easily models FOAF networks. By assigning different weights to the links according to authors coauthoring history, we show that recency is helpful in predicting the formation of new links.