Characterizing heterogeneity in cooperative networks from a resource distribution view-point

A network of agents in which agents with a diverse set of resources or capabilities interact and coordinate with each other to accomplish various tasks constitutes a heterogeneous cooperative network. In this paper, we investigate heterogeneity in terms of resources allocated to agents within the network. The objective is to distribute resources in such a way that every agent in the network should be able to utilize all these resources through local interactions. In particular, we formulate a graph coloring problem in which each node is assigned a subset of labels from a labeling set, and a graph is considered to be completely heterogeneous whenever all the labels in the labeling set are available in the closed neighborhood of every node. The total number of different resources that can be accommodated within a system under this setting depends on the underlying graph structure of the network. This paper provides an analysis of the assignment of multiple resources to nodes and the effect of these assignments on the overall heterogeneity of the network.