Random rectangular graphs.

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...

Probability Density Function of the Euclidean Distance between Node Pairs in Rectangular Random Graphs and its Applications in MANETs

This paper focuses on the probability density function of the Euclidean distance between node pairs in rectangular random graphs. As the main achievement of the paper, a closed analytic formula of the probability density function of the Euclidean distance between node pairs in rectangular random graphs was obtained basing on combinatorial theory and asymptotic concept. Some lemmas, such as numb...

Rectangular Matrix Models and Combinatorics of Colored Graphs

We present applications of rectangular matrix models to various combinatorial problems, among which the enumeration of face-bicolored graphs with prescribed vertex degrees, and vertex-tricolored triangulations. We also mention possible applications to Interaction-Round-a-Face and hard-particle statistical models defined on random lattices.

M ar 2 01 5 Random Rectangular Graphs

Random neighborhood graphs as models of fracture networks on rocks: Structural and dynamical analysis

We propose a new model to account for the main structural characteristics of rock fracture networks (RFNs). The model is based on a generalization of the random neighborhood graphs to consider fractures embedded into rectangular spaces. We study a series of 29 real-world RFNs and find the best fit with the random rectangular neighborhood graphs (RRNGs) proposed here. We show that this model cap...