Cognition-inspired graph theory: Vertex routing models and recursive clique graphs

We report work in progress on a new class of vertex routing models and on recursive clique graphs, which are both motivated by our long-term research on cognitive system theory.

Information arriving to a vertex B arriving from a vertex A is routed to vertex C in a vertex routing model. We define a class of random vertex routing models with and without a memory trace and the notion of information centrality based on the long-term information flow in terms of cyclic attractors. We find that the information centrality is extensive/sub-extensive for models with/without a memory trace.

A clique is a maximal fully connected subgraph and a clique graph is the meta-network of cliques. We study numerically the possible occurrence of a phase-transition in recursive clique graphs with respect to their growth properties, starting from Erdös-Renyi graphs, as a function of the initial connectivity.