Random rectangular graphs

Random rectangular graphs.

A generalization of the random geometric graph (RGG) model is proposed by considering a set of points uniformly and independently distributed on a rectangle of unit area instead of on a unit square [0,1](2). The topological properties of the random rectangular graphs (RRGs) generated by this model are then studied as a function of the rectangle sides lengths a and b=1/a, and the radius r used t...

Synchronizability of random rectangular graphs.

Random rectangular graphs (RRGs) represent a generalization of the random geometric graphs in which the nodes are embedded into hyperrectangles instead of on hypercubes. The synchronizability of RRG model is studied. Both upper and lower bounds of the eigenratio of the network Laplacian matrix are determined analytically. It is proven that as the rectangular network is more elongated, the netwo...

Consensus dynamics on random rectangular graphs

A random rectangular graph (RRG) is a generalization of the random geometric graph (RGG) in which the nodes are embedded into a rectangle with side lengths a and b = 1/a, instead of on a unit square [0, 1]2 . Two nodes are then connected if and only if they are separated at a Euclidean distance smaller than or equal to a certain threshold radius r . When a = 1 the RRG is identical to the RGG. H...

M ar 2 01 5 Random Rectangular Graphs

Products of Random Rectangular Matrices

We study the asymptotic behaviour of points under matrix cocyles generated by rectangular matrices. In particular we prove a random Perron-Frobenius and a Multiplicative Ergodic Theorem. We also provide an example where such products of random rectangular matrices arise in the theory of random walks in random environments and where the Multiplicative Ergodic Theorem can be used to investigate r...