Construction of edge-ordered multidirected graphlets for comparing dynamics of spatial temporal neural networks

The integration and transmission of information in the brain are dependent on the interplay between structural and dynamical properties. Implicit in any pursuit aimed at understanding neural dynamics from appropriate sets of mathematically bounded conditions is the notion of an underlying fundamental structure-function constraint imposed by the geometry of the structural networks and the resultant latencies involved with transfer of information. We recently described the construction and theoretical analysis of a framework that models how local structure-function rules give rise to emergent global dynamics on a neural network. An important part of this research program is the requirement for a set of mathematical methods that allow us to catalog, theoretically analyze, and numerically study the rich dynamical patterns that result. One direction we are exploring is an extension of the theory of graphlets. In this paper we introduce an extension of graphlets and associated metric that maps the topological transition of a network from one moment in time to another at the same time that causal relationships are preserved.