Groupies in multitype random graphs

Groupies in Random Bipartite Graphs

A vertex of a graph G is called a groupie if its degree is not less than the arithmetic mean of the degrees of its neighbors. Some results concerning groupies have been obtained in deterministic graph theory; see e.g. [1, 5, 6]. Recently, Fernandez de la Vega and Tuza [3] investigate groupies in Erdős-Rényi random graphs G(n, p) and shows that the proportion of the vertices which are groupies i...

Central Limit Theorem in Multitype Branching Random Walk

A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.

Multitype Randomized Reed–frost Epidemics and Epidemics upon Random Graphs

We consider a multitype epidemic model which is a natural extension of the randomized Reed–Frost epidemic model. The main result is the derivation of an asymptotic Gaussian limit theorem for the final size of the epidemic. The method of proof is simpler, and more direct, than is used for similar results elsewhere in the epidemics literature. In particular, the results are specialized to epidemi...

On groupies in graphs

Suppressing cascades of load in interdependent networks.

Understanding how interdependence among systems affects cascading behaviors is increasingly important across many fields of science and engineering. Inspired by cascades of load shedding in coupled electric grids and other infrastructure, we study the Bak-Tang-Wiesenfeld sandpile model on modular random graphs and on graphs based on actual, interdependent power grids. Starting from two isolated...