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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 ..."
Abstract

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
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 ..."
Abstract
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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.