Fast unfolding of communities in large networks

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Abstract

We propose a simple method to extract the community structure of large networks. Our method is a heuristic method that is based on modularity optimization. It is shown to outperform all other known community detection method in terms of computation time. Moreover, the quality of the communities detected is very good, as measured by the so-called modularity. This is shown first by identifying language communities in a Belgian mobile phone network of 2.6 million customers and by analyzing a web graph of 118 million nodes and more than one billion links. The accuracy of our algorithm is also verified on ad-hoc modular networks. .

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Statistical mechanics of complex networks

Reka Albert, Albert-László Barabási (2001)

Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.

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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

Michelle Girvan, M. Newman (2001)

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.