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. 2019 Nov 8;10:5107. doi: 10.1038/s41467-019-13006-7

Fig. 1.

Fig. 1

Isothermal graphs and their effective degrees. A graph is isothermal if the sum of edge weights is the same for each vertex. The effective degree κ~ of the graph, defined in Eq. (3), determines the outcome of evolutionary game dynamics. a An asymmetric isothermal graph; weights are shown for each edge. b A wheel graph, with one hub and n wheel vertices. All connections with the hub have weight 1n. All connections in the periphery have weight (n1)2n. As n, the effective degree approaches 2. A formula for arbitrary n is derived in Supplementary Note 3. c A 30-vertex graph generated with preferential attachment62 and linking number m=3. Isothermal edge weights are obtained by quadratic programming (see Methods). The effective degree, κ~2.47, is less than the average topological degree, k¯=5.6. d An island model, with edges of weight α1 between each inter-island pair of vertices. Shown here are two islands: a k1-regular graph of size N1, and a k2-regular graph of size N2