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Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such
Detecting the overlapping and hierarchical community structure in complex networks
 New J. Phys. p
, 2009
"... Abstract. Many networks in nature, society and technology are characterized by a mesoscopic level of organization, with groups of nodes forming tightly connected units, called communities or modules, that are only weakly linked to each other. Uncovering this community structure is one of the most im ..."
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Cited by 143 (0 self)
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Abstract. Many networks in nature, society and technology are characterized by a mesoscopic level of organization, with groups of nodes forming tightly connected units, called communities or modules, that are only weakly linked to each other. Uncovering this community structure is one of the most important problems in the field of complex networks. Networks often show a hierarchical organization, with communities embedded within other communities; moreover, nodes can be shared between different communities. Here we present the first algorithm that finds both overlapping communities and the hierarchical structure. The method is based on the local optimization of a fitness function. Community structure is revealed by peaks in the fitness histogram. The resolution can be tuned by a parameter enabling to investigate different hierarchical levels of organization. Tests on real and artificial networks give excellent results. PACS numbers: 89.75.k, 89.75.Hc, 05.40a, 89.75.Fb, 87.23.GeDetecting the overlapping and hierarchical community structure in complex networks 2 1.
Comparative Evaluation of Community Detection Algorithms: A Topological Approach
, 2012
"... Abstract: Community detection is one of the most active fields in complex networks analysis, due to its potential value in practical applications. Many works inspired by different paradigms are devoted to the development of algorithmic solutions allowing to reveal the network structure in such cohes ..."
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Cited by 8 (2 self)
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Abstract: Community detection is one of the most active fields in complex networks analysis, due to its potential value in practical applications. Many works inspired by different paradigms are devoted to the development of algorithmic solutions allowing to reveal the network structure in such cohesive subgroups. Comparative studies reported in the literature usually rely on a performance measure considering the community structure as a partition (Rand Index, Normalized Mutual information, etc.). However, this type of comparison neglects the topological properties of the communities. In this article, we present a comprehensive comparative study of a representative set of community detection methods, in which we adopt both types of evaluation. Communityoriented topological measures are used to qualify the communities and evaluate their deviation from the reference structure. In order to mimic realworld systems, we use artificially generated realistic networks. It turns out there is no equivalence between both approaches: a high performance does not necessarily correspond to correct topological properties, and viceversa. They can therefore be considered as complementary, and we recommend applying both of them in order to perform a complete and accurate assessment. 1.
Contents
, 903
"... We consider an Abelian Gauge Theory in R 4 equipped with the Minkowski metric. This theory leads to a system of equations, the KleinGordonMaxwell equations, which provide models for the interaction between the electromagnetic field and matter. We assume that the nonlinear term is such that the ene ..."
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We consider an Abelian Gauge Theory in R 4 equipped with the Minkowski metric. This theory leads to a system of equations, the KleinGordonMaxwell equations, which provide models for the interaction between the electromagnetic field and matter. We assume that the nonlinear term is such that the energy functional is positive; this fact makes the theory more suitable for physical models. A three dimensional vortex is a finite energy, stationary solution of these equations such that the matter field has nontrivial angular momentum and the magnetic field looks like the field created by a finite solenoid. Under suitable assumptions, we prove the existence of three dimensional vortexsolutions.