Topological versus spectral properties of random geometric graphs

Spectral Analysis of Virus Spreading in Random Geometric Graphs

In this paper, we study the dynamics of a viral spreading process in random geometric graphs (RGG). In an RGG, nodes are randomly distributed in a particular spatial region, and edges are located between those pairs of nodes that lie within a given distance r from each other. The spreading of the viral process we consider in this paper is closely related with the spectral radius of the adjacenc...

Topological properties of the one dimensional exponential random geometric graph

Topological Properties of an Exponential Random Geometric Graph Process

In this paper we consider a one-dimensional random geometric graph process with the inter-nodal gaps evolving according to an exponential AR(1) process. The transition probability matrix and stationary distribution are derived for the Markov chains concerning connectivity and the number of components. We analyze the algorithm for hitting time regarding disconnectivity. In addition to dynamical ...

Geometric and spectral properties of locally tessellating planar graphs

In this article, we derive bounds for values of the global geometry of locally tessellating planar graphs, namely, the Cheeger constant and exponential growth, in terms of combinatorial curvatures. We also discuss spectral implications for the Laplacians.

Spectral and Geometric Properties of k-Walk-Regular Graphs

Let us consider a connected graph G with diameter D. For a given integer k between 0 and D, we say that G is k-walk-regular if the number of walks of length between vertices u, v only depends on the distance between u and v, provided that such a distance does not exceed k. Thus, in particular, a 0-walk-regular graph is the same as a walk-regular graph, where the number of cycles of length roote...