Percolation theory can be used to describe the structural properties of complex networks using generating function formulation. This mapping assumes that network is locally treelike and does not contain short-range loops between neighbors. In this paper we use formulation examine clustered simple cycles cliques any order. We natural generalization Molloy-Reed criterion for these their critical ...

We introduce a new class of games, Random Order Congestion Games [ROCGs]. In an ROCG, each player has a task that can be carried out by any element of a set of resources, and each resource executes its assigned tasks in a random order. Each player’s aim is to minimize his expected cost which is the sum of two terms – the sum of the fixed costs over the set of his utilized resources and the expe...

Our main results are quantitative bounds in the multivariate normal approximation of centred subgraph counts random graphs generated by a general graphon and independent vertex labels. We interested these statistics because they key to understanding fluctuations regular — cornerstone dense graph limit theory. also identify resulting limiting Gaussian stochastic measures means theory generalised...

The chemical short-range order (CSRO) in crystalline materials influences the properties, and its effect is significant context of multicomponent materials. We propose a scheme for CSRO parameter or ∆-parameter terms number like unlike bonds systems. OPERA Order Parameter Engineering RAndom Systems semi-canonical canonical ensembles proposed. proposed framework with can generate single-phase su...