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      Defining and evaluating network communities based on ground-truth

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      Knowledge and Information Systems

      Springer Nature

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          The Strength of Weak Ties

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            Modularity and community structure in networks

             M. Newman (2006)
            Many networks of interest in the sciences, including a variety of social and biological networks, are found to divide naturally into communities or modules. The problem of detecting and characterizing this community structure has attracted considerable recent attention. One of the most sensitive detection methods is optimization of the quality function known as "modularity" over the possible divisions of a network, but direct application of this method using, for instance, simulated annealing is computationally costly. Here we show that the modularity can be reformulated in terms of the eigenvectors of a new characteristic matrix for the network, which we call the modularity matrix, and that this reformulation leads to a spectral algorithm for community detection that returns results of better quality than competing methods in noticeably shorter running times. We demonstrate the algorithm with applications to several network data sets.
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              Community structure in social and biological networks

              A number of recent studies have focused on the statistical properties of networked systems such as social networks and the World-Wide Web. Researchers have concentrated particularly on a few properties which seem to be common to many networks: the small-world property, power-law degree distributions, and network transitivity. In this paper, we highlight another property which is found in many networks, the property of community structure, in which network nodes are joined together in tightly-knit groups between which there are only looser connections. We propose a new method for detecting such communities, built around the idea of using centrality indices to find community boundaries. We test our method on computer generated and real-world graphs whose community structure is already known, and find that it detects this known structure with high sensitivity and reliability. We also apply the method to two networks whose community structure is not well-known - a collaboration network and a food web - and find that it detects significant and informative community divisions in both cases.
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                Author and article information

                Journal
                Knowledge and Information Systems
                Knowl Inf Syst
                Springer Nature
                0219-1377
                0219-3116
                January 2015
                October 2013
                : 42
                : 1
                : 181-213
                10.1007/s10115-013-0693-z
                © 2015
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