Fig. 1. The calculation of equivalent conductance between any pair of nodes in a complete network.完全网络任意一对节点之间等效电导的计算过程

Fig. 2. Dependence of (a) communicability sequence entropy and (b) mean global conductance on rewiring probability of WS small-world network; (c) , (d) the relation between and of WS small-world network. WS小世界网络的(a)通信序列熵 和(b) 平均全局电导 与重连概率 的依赖关系; (c), (d)相应的 与 之间的关系

Fig. 3. The dependence of (a) communicability sequence entropy and (b) mean global conductance on degree distribution exponent of scale-free network; (c), (d) the results of mapping with in the same coordinate system. 无标度网络的(a)通信序列熵 和(b)平均全局电导 与度分布指数 的依赖关系; (c), (d) 将 与 映射在同一坐标系下的结果

Fig. 4. Dependence of communicability sequence entropy of the scale-free network on the degree-degree correlation coefficient , here, the degree distribution exponent is equal to (a) 2.5 and (d) 3.0, respectively; (b), (e) the dependence of the mean global conductance on the correlation coefficient ; (c), (f) the and relation curve. 度分布指数 分别等于(a) 2.5和(d) 3.0时的关联无标度网络的通信序列熵 与度-度关联系数 的依赖关系; 相应的平均全局电导 与关联系数 的依赖关系, 分别等于(b) 2.5和(e) 3.0; (c), (f) 与 的关系曲线

Fig. 5. A visualization of the community network based on the BA network. The number of communities is 1 to 6, which are denoted as C1 to C6. The generation method of the community network in each network in the figure is generated according to the method of Ref. [7]. The network size is , the number of network edges is . The specific algorithm is as follows: 1) First, a BA network with 900 nodes and 2700 edges is generated, as shown in figure C1; 2) two BA networks containing 450 nodes and 1350 edges are generated, and then a small number of edges are randomly disconnected in each community, and these disconnected edges are connected to the endpoints of the interrupted edges of other communities to form a network C2 containing two communities; 3) in this way, BA network C3, C4, C5 and C6 containing 3, 4, 5 and 6 communities can be generated.ntaining 3, 4, 5 and 6 communities can be generated. 以BA网络为例构建的社团网络可视化图, 社团个数为1—6, 分别表示为C1—C6. 图中每一个网络中社团网络的生成方式都是按照文献[7]的方法生成. 网络规模 , 网络边数 . 具体算法如下: 1)首先生成一个含有900个节点, 2700条边的BA网络(图C1); 2)生成两个含有450个节点、1350条边的BA网络, 然后在每个社团中随机断开少量的边, 并将这些断开的边连接到其他社团中断开的边的端点上, 形成一个含有两个社团的网络C2; 3)以此类推, 便可生成含有3, 4, 5, 6个社团的BA网络C3, C4, C5, C6

Table 1. Relationship between communicability sequence entropy , mean global conductance and number of communities in networks [BA (left), ER (right)] containing communities. 含有社团结构的网络[BA (左), ER (右)]通信序列熵 、平均全局电导 与社团个数的关系

Table 2. Power supply network and corresponding randomized reference model and mean global conductance , IEEE57 (left), IEEE118 (right). 电力供需网络以及对应的随机化参考模型的 和平均电导 , IEEE57 (左), IEEE118 (右)