Joint talk: Dimitri Volchenkov (Texas Tech University) & Steve Suh (Texas Agriculture & Machinery University)
Abstract: We study the thermodynamic limit of infinite walks on finite, non-random graphs. As walks represent chains of interactions between system units, statistical mechanics of long walks may be used to quantify the structurally anchored network functions, as well as accessibility, controllability, feedback, and navigability in networks. Openness of a network to structural modifications is characterized by a Fermi-Dirac distribution of nodes relative fugacity in the framework of grand canonical ensemble of walks. The same distributions appear as the stationary solutions of the Fokker –Planck equations describing network flows under random rewiring of edges and noise.
In complex network theory, the high centrality nodes (at any measure) are more influential, especially in accumulating new connections. However, in dynamic complex networks, structural modifications associated with vertices of high fugacity (and minimal centrality) are most likely, as they change minimally the system of long walks in graphs that is critical for reliable network functioning.