Figure 1

The fraction of vertices correctly identified by our algorithms in the computer-generated graphs described in the text. The two curves show results for our algorithm (circles) and for the algorithm of Girvan and Newman [5] (squares). Each point is an average over 100 graphs.Reuse & Permissions

Figure 2

Dendrogram of the communities found by our algorithm in the “karate club” network of Zachary [5, 17]. The shapes of the vertices represent the two groups into which the club split as the result of an internal dispute.Reuse & Permissions

Figure 3

Dendrogram of the communities found in the college football network descibed in the text. The real-world communities—conferences—are denoted by the different shapes as indicated in the legend.Reuse & Permissions

Figure 4

Left panel: Community structure in the collaboration network of physicists. The graph breaks down into four large groups, each composed primarily of physicists of one specialty, as shown. Specialties are determined by the subsection(s) of the e-print archive in which individuals post papers: “C.M.” indicates condensed matter; “H.E.P.” indicates high-energy physics including theory, phenomenology, and nuclear physics; “astro” indicates astrophysics. Middle panel: one of the condensed matter communities is further broken down by the algorithm, revealing an approximate power-law distribution of community sizes. Right panel: one of these smaller communities is further analyzed to reveal individual research groups (different shades), one of which (in the dashed box) is the author’s own.Reuse & Permissions

Figure 5

Cumulative distribution function of the sizes of communities found in one of the subnetworks of the physics collaboration graph, as described in the text. The dotted line represents the slope the plot would have if the distribution followed a power law with exponent $-1.6$.Reuse & Permissions