Symmetrical threshold model with independence on random graphs

Randomized Consensus Processing over Random Graphs: Independence and Threshold

In this paper, we study randomized consensus processing over general random graphs. At time step k, each node will follow the standard consensus algorithm, or stick to current state by a simple Bernoulli trial with success probability pk. Connectivity-independent and arc-independent graphs are defined, respectively, to capture the fundamental independence of random graph processes with respect ...

On the independence number of random graphs

Random Threshold Graphs

We introduce a pair of natural, equivalent models for random threshold graphs and use these models to deduce a variety of properties of random threshold graphs. Specifically, a random threshold graph G is generated by choosing n IID values x1, . . . , xn uniformly in [0, 1]; distinct vertices i, j of G are adjacent exactly when xi + x j > 1. We examine various properties of random threshold gra...

Threshold Graph Limits and Random Threshold Graphs

We study the limit theory of large threshold graphs and apply this to a variety of models for random threshold graphs. The results give a nice set of examples for the emerging theory of graph limits.

Threshold Phenomena in Random Graphs

We consider a model of Random Graphs by Erdős and Rényi [ER60]. To generate a random graph with n vertices, for every pair of vertices {i, j}, we put an edge independently with probability p. This model is denoted by Gn,p. Let G be a random Gn,p graph and let H be any fixed graph (on some constant number of vertices independent of n). We will be interested in understanding the probability that ...