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Review
. 2002 Jun 11;99(12):7821-6.
doi: 10.1073/pnas.122653799.

Community structure in social and biological networks

M Girvan  1 , M E J Newman
Affiliations
Review

Community structure in social and biological networks

M Girvan et al. Proc Natl Acad Sci U S A. .

Abstract

A number of recent studies have focused on the statistical properties of networked systems such as social networks and the Worldwide Web. Researchers have concentrated particularly on a few properties that seem to be common to many networks: the small-world property, power-law degree distributions, and network transitivity. In this article, we highlight another property that 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 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 the method 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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Figures

Figure 1
Figure 1
A schematic representation of a network with community structure. In this network there are three communities of densely connected vertices (circles with solid lines), with a much lower density of connections (gray lines) between them.
Figure 2
Figure 2
An example of a small hierarchical clustering tree. The circles at the bottom represent the vertices in the network, and the tree shows the order in which they join together to form communities for a given definition of the weight Wij of connections between vertex pairs.
Figure 3
Figure 3
The fraction of vertices correctly classified in computer-generated graphs of the type described in the text, as the average number of intercommunity edges per vertex is varied. The circles are results for the method presented in this article; the squares are for a standard hierarchical clustering calculation based on numbers of edge-independent paths between vertices. Each point is an average over 100 realizations of the graphs. Lines between points are included solely as a guide to the eye.
Figure 4
Figure 4
(a) The friendship network from Zachary's karate club study (26) as described in the text. Nodes associated with the club administrator's faction are drawn as circles, those associated with the instructor's faction are drawn as squares. (b) Hierarchical tree showing the complete community structure for the network calculated by using the algorithm presented in this article. The initial split of the network into two groups is in agreement with the actual factions observed by Zachary, with the exception that node 3 is misclassified. (c) Hierarchical tree calculated by using edge-independent path counts, which fails to extract the known community structure of the network.
Figure 5
Figure 5
Hierarchical tree for the network reflecting the schedule of regular-season Division I college football games for year 2000. Nodes in the network represent teams, and edges represent games between teams. Our algorithm identifies nearly all of the conference structure in the network.
Figure 6
Figure 6
The largest component of the Santa Fe Institute collaboration network, with the primary divisions detected by our algorithm indicated by different vertex shapes.
Figure 7
Figure 7
Hierarchical tree for the Chesapeake Bay food web described in the text.
See this image and copyright information in PMC

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