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. 2016 Jan 15;113(5):1435–1440. doi: 10.1073/pnas.1513302113

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Fig. S1. — Hub connectivity is topologically central and costly. Each plot shows the variation of a network property as a function of the number of connections (or degree k) at which hubs (regions with degree $> k$ ) are defined. A, Upper, C, Upper, and E, Upper show the degree distribution of the mouse connectome for ease of comparison with each plot. (A) Normalized rich club coefficient, $Φ_{norm}$ , as in Fig. 2B reproduced here for ease of comparison. Circles indicate values of $Φ_{norm}$ that are statistically higher than an ensemble of 10,000 null networks (permutation test; $P < 0.05$ ). The topological rich regime ( $42 \leq k \leq 54$ ) is shaded gray in all figures. (B) The proportion of brain regions with degree $> k$ in each of 13 broad anatomical divisions from the Allen Mouse Brain Atlas (24, 26) as a function of k. (C–F) The remaining plots summarize other mean properties of links connecting regions with degree $> k$ , with circles indicating statistically significant increases relative to values assigned to all other network links (Welch’s t test; $P < 0.05$ ): (C) connection distance (millimeters), (D) reciprocal connectivity, (E) $\log_{10}$ connectivity weight, and (F) communicability (line) (47) and edge betweenness centrality (dashed line) (46). Each of these properties increases with k and is elevated across the topological rich club regime, indicating a high centrality and cost of connections between hub regions.