We prove a quantitative Russo-Seymour-Welsh (RSW) type result for random walks on two natural examples of random planar graphs: the supercritical percolation cluster in the square lattice and the ...

MARC NOY, VLADY RAVELOMANANA, JUANJO RUÉ, ON THE PROBABILITY OF PLANARITY OF A RANDOM GRAPH NEAR THE CRITICAL POINT, Proceedings of the American Mathematical Society, Vol. 143, No. 3 (MARCH 2015), pp.

Chatterjee et al. (2011) established the consistency of the maximum likelihood estimator in the β-model for undirected random graphs when the number of vertices goes to infinity. By approximating the ...

Random graphs constitute one specific case — a random graph can be thought of as a random subset of the set of all possible edges — but there are many other objects that fall within the conjecture’s ...

Node classification, as a central task in the graph data analysis, has been studied extensively with network embedding technique for single-layer graph network. However, there are some obstacles when ...