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Community Structure in Graphs
Santo Fortunato,Claudio Castellano +1 more
- pp 1141-1163
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TLDR
In this article, the problem of detecting communities in a graph is discussed, both conceptually and practically, due to the ambiguity in the definition of community and in the discrimination of different partitions and algorithms must find good partitions among an exponentially large number of them.Abstract:
Graph vertices are often organized into groups that seem to live fairly independently of the rest of the graph, with which they share but a few edges, whereas the relationships between group members are stronger, as shown by the large number of mutual connections. Such groups of vertices, or communities, can be considered as independent compartments of a graph. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. The task is very hard, though, both conceptually, due to the ambiguity in the definition of community and in the discrimination of different partitions and practically, because algorithms must find “good” partitions among an exponentially large number of them. Other complications are represented by the possible occurrence of hierarchies, i.e. communities which are nested inside larger communities, and by the existence of overlaps between communities, due to the presence of nodes belonging to more groups. All these aspects are dealt with in some detail and many methods are described, from traditional approaches used in computer science and sociology to recent techniques developed mostly within statistical physics.read more
Citations
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Journal ArticleDOI
Stability of graph communities across time scales.
TL;DR: In this paper, the authors introduce the stability of a partition, a measure of its quality as a community structure based on the clustered autocovariance of a dynamic Markov process taking place on the network.
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Comparing Community Structure to Characteristics in Online Collegiate Social Networks
TL;DR: This study examines the importance of common high school affiliation at large state universities and the varying degrees of influence that common major can have on the social structure at different universities, indicating that university networks typically have multiple organizing factors rather than a single dominant one.
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Laplacian Dynamics and Multiscale Modular Structure in Networks
TL;DR: In this article, the stability of a network partition is defined in terms of the statistical properties of a dy namical process taking place on the graph, and the connection between community detection and Laplacian dynamics enables them to establish dynamically motivated stability measures linked to distinct null models.
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Extending the definition of modularity to directed graphs with overlapping communities
TL;DR: This paper starts from the definition of a modularity function, given by Newman to evaluate the goodness of network community decompositions, and extends it to the more general case of directed graphs with overlapping community structures.
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A classification for community discovery methods in complex networks
TL;DR: The aim of this survey is to provide a ‘user manual’ for the community discovery problem and to organize the main categories of community discovery methods based on the definition of community they adopt.
References
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