ELASTICITY: Topological Characterization of Robustness in Complex Networks

Just as a herd of animals relies on its robust social structure to survive in the wild, similarly robustness is a crucial characteristic for the survival of a complex network under attack. The capacity to measure robustness in complex networks defines the resolve of a network to maintain functionality in the advent of classical component failures and at the onset of cryptic malicious attacks. To date, robustness metrics are deficient and unfortunately the following dilemmas exist: accurate models necessitate complex analysis while conversely, simple models lack applicability to our definition of robustness. In this paper, we define robustness and present a novel metric, elasticity- a bridge between accuracy and complexity-a link in the chain of network robustness. Additionally, we explore the performance of elasticity on Internet topologies and online social networks, and articulate results

Restricted connectivity of cartesian products of some graphs

A vertex cut S of G is said to be a restricted vertex cut if NG(u) - S , ? for any vertex u of G. If G has a restricted vertex cut, then the minimum cardinality of them called the restricted connectivity of G and we denote the restricted connectivity of G by ′(G); this is a more refined index than the connectivity parameter (G). In this paper, we prove that 2 1 + 2 2 ?? 2 ?? t1 ?? t2 ′(G1 G2) Δ1 + 1 + 2 2 ?? 2, where, for i = 1; 2, Gi is a maximally connected (Kti+1 + K2) - free graph such that (Gi) 2, V(Gi) 2 i ?? ti, and Δ1 + 2 Δ2 + 1,where i = i(G) and Δi = Δi(G) for i = 1; 2.電気通信大学201