  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.
