We consider random processes more general than those considered by Erdös and Rényi for generating the countable random graph. It is proved that, in the category sense, almost all random processes we consider generate the countable random graph with probability 1. Under a weak boundedness assumption we give a criterion for the random processes which generate the countable random graph almost sur...

This paper proposes a concept of uncertain random graph in which some edges exist with some degrees in probability measure and others exist with some degrees in uncertain measure, and discusses the connectivity index of an uncertain random graph. In addition, this paper presents a concept uncertain random network in which some weights are random variables and others are uncertain variables, and...

the dispersibility of graphene is modeled as a mathematical function of the molecular structure of solvent represented by simplified molecular input-line entry systems (smiles) together with the graph of atomic orbitals (gao). the gao is molecular graph where atomic orbitals e.g. 1s1, 2p4, 3d7 etc., are vertexes of the graph instead of the chemical elements used as the graph vertexes in the tra...

The goal of this paper is to establish a connection between two classical models of random graphs: the random graph G(n, p) and the random regular graph Gd(n). This connection appears to be very useful in deriving properties of one model from the other. In particular, one immediately obtains one-line proofs of several highly non-trivial and recent results on Gd(n).