Maximal assortative matching for real-world network graphs, random network graphs and scale-free network graphs

On the Conduciveness of Random Network Graphs for Maximal Assortative or Maximal Dissortative Matching

A maximal matching of a graph is the set of edges such that the addition of an edge to this set violates the property of matching (i.e., no two edges of the matching share a vertex). We use the notion of assortative index (ranges from -1 to 1) to evaluate the extent of similarity of the end vertices constituting the edges of a matching. A maximal matching of the edges whose assortative index is...

Random maximal H-free graphs

Sensor Network Self-Organization Using Random Graphs

RANDOM graph theory originated with seminal work by Erdös and Re nyi in the 1950s. Until then, graph theory analyzed either specific graph instances or deterministically defined graph classes. Erdös and Re nyi considered graph classes where the existence of edges between nodes was determined probabilistically. Their results were theoretically interesting and found applications in many practical...

Probabilistic Diffusion in Random Network Graphs

In this paper, we consider a random network such that there could be a link between any two nodes in the network with a certain probability (plink). Diffusion is the phenomenon of spreading information throughout the network, starting from one or more initial set of nodes (called the early adopters). Information spreads along the links with a certain probability (pdiff). Diffusion happens in ro...

Balanced Graphs and Network

A graph G is balanced if the maximum ratio of edges to vertices, taken over all subgraphs of G, occurs at G itself. This note uses the maxow/min-cut theorem to prove a good characterization of balanced graphs. This characterization is then applied to some results on how balanced graphs may be combined to form a larger balanced graph. In particular, we show that edge-transitive graphs and comple...