TY - JOUR

T1 - Communicability angles reveal critical edges for network consensus dynamics

AU - Estrada, Ernesto

AU - Vargas-Estrada, Eusebio

AU - Ando, Hiroyasu

N1 - Publisher Copyright:
© 2015 American Physical Society.

PY - 2015/11/19

Y1 - 2015/11/19

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84949239356&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.92.052809

DO - 10.1103/PhysRevE.92.052809

M3 - Article

AN - SCOPUS:84949239356

SN - 1539-3755

VL - 92

JO - Physical Review E

JF - Physical Review E

IS - 5

M1 - 052809

ER -