The standard Erd˝os-Renyi model of random graphs begins with n isolated vertices, and at each round a random edge is added. Parametrizing n 2 rounds as one time unit, a phase tra...
Estimating characteristics of large graphs via sampling is a vital part of the study of complex networks. Current sampling methods such as (independent) random vertex and random w...
Two classic “phase transitions” in discrete mathematics are the emergence of a giant component in a random graph as the density of edges increases, and the transition of a rand...
The intrinsically secure communications graph (-graph) is a random graph which captures the connections that can be securely established over a large-scale network, in the presence...
In this paper, we investigate limiting behavior of linear dynamic systems driven by random stochastic matrices. We introduce and study the new concepts of partial ergodicity and 1-...