title: Network reliability: the effect of local network structure on diffusive processes.
abstract: This paper reintroduces the network reliability polynomial, introduced by Moore and Shannon [Moore and Shannon, J. Franklin Inst. 262, 191 (1956)], for studying the effect of network structure on the spread of diseases. We exhibit a representation of the polynomial that is well suited for estimation by distributed simulation. We describe a collection of graphs derived from Erdős-Rényi and scale-free-like random graphs in which we have manipulated assortativity-by-degree and the number of triangles. We evaluate the network reliability for all of these graphs under a reliability rule that is related to the expected size of a connected component. Through these extensive simulations, we show that for positively or neutrally assortative graphs, swapping edges to increase the number of triangles does not increase the network reliability. Also, positively assortative graphs are more reliable than neutral or disassortative graphs with the same number of edges. Moreover, we show the combined effect of both assortativity-by-degree and the presence of triangles on the critical point and the size of the smallest subgraph that is reliable.
authors: Network Dynamics and Simulation Science Laboratory, Virginia Bioinformatics Institute, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, USA.
authors: Mina
authors: M
authors: Youssef
authors: Network Dynamics and Simulation Science Laboratory, Virginia Bioinformatics Institute, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, USA and Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, USA.
authors: Yasamin
authors: Y
authors: Khorramzadeh
authors: Network Dynamics and Simulation Science Laboratory, Virginia Bioinformatics Institute, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, USA and Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, USA and Department of Population Health Sciences, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, USA.
authors: Stephen
authors: S
authors: Eubank