Communicability Angles Reveal Critical Edges for Network Consensus Dynamics
Communicability Angles Reveal Critical Edges for Network Consensus Dynamics
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DOI：
10.1103/physreve.92.052809
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发表时间：
2015-07
期刊：
影响因子：
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通讯作者：
Ernesto Estrada;Eusebio Vargas-Estrada;H. Ando
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文献类型：
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作者：
Ernesto Estrada;Eusebio Vargas-Estrada;H. Ando
我们考虑确定拓扑结构如何影响发生在网络上的共识动态过程的问题。通过考虑现实世界网络的大型数据集，我们首先确定根据其可通信角（欧几里得可通信空间中节点位置向量之间的角度）去除边缘，使现实世界网络的平均共识时间增加了5.68倍。边缘中间性中心性还以较小的比例识别共识动态的关键边缘；也就是说，它的移除使达成共识的时间增加了3.70倍。基于代数连通性和网络的等周数对所研究的动力学过程的作用以及它们与上述性质的联系，我们从理论上证明了这些发现。最后，研究了网络全局拓扑参数对共识动力学的影响。我们确定网络密度和平均距离和（类似于最短路径距离的节点度）在研究的现实世界网络中占平均共识时间方差的80%以上。
We consider the question of determining how the topological structure influences a consensus dynamical processes taking place on a network. By considering a large data set of real-world networks we first determine that the removal of edges according to their communicability angle, an angle between position vectors of the nodes in an Euclidean communicability space, increases the average time of consensus by a factor of 5.68 in real-world networks. The edge betweenness centrality also identifies, in a smaller proportion, those critical edges for the consensus dynamics; i.e., its removal increases the time of consensus by a factor of 3.70. We justify theoretically these findings on the basis of the role played by the algebraic connectivity and the isoperimetric number of networks on the dynamical process studied and their connections with the properties mentioned before. Finally, we study the role played by global topological parameters of networks on the consensus dynamics. We determine that the network density and the average distance-sum, which is analogous of the node degree for shortest-path distances, account for more than 80% of the variance of the average time of consensus in the real-world networks studied.