Novel Resistive Distance Descriptors on Complex Network

Abstract

Large-scale complex network data poses significant challenges for the analytic ideas and tools to monitor and analyze complex networks. As classical structure descriptors, average path length ( $L$ ), global and local network efficiency ( $E_{glob}$ and $E_{loc}$ ), general and loop clustering coefficient ( $C_{3}$ and $D$ ), play significant roles in complex network analysis. In this paper, we make use of resistive distance instead of the shortest path distance to suggest resistive distance descriptors, i.e., $L_{r}$ , $\Omega _{glob}$ and $\Omega _{loc}$ , $\Omega _{3}$ and $D_{r}$ . We investigate all the resistive descriptors on classical WS, BA and ER models and find some interesting phenomenons. On one hand, $L_{r}$ and $\Omega _{3}$ (resp., $\Omega _{glob}$ and $\Omega _{loc}$ ) can be used to characterize the features of small-word networks. On the other hand, $L_{r}$ , $\Omega _{3}$ , and $\Omega _{glob}$ can be utilized to measure network invulnerability. To access the effectiveness of the resistive distance descriptors, we conduct extensive numerical simulations on synthetic and real networks. In comparison with the baselines, the proposed metrics show competitive performance on classical network models and are more efficient for networks with small and medium size.

Keywords

• Resistive distance
• clustering coefficient
• network efficiency
• network invulnerability