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In this paper, we present a novel thermodynamic framework for graphs that can be used to analyze time evolving networks, relating the thermodynamics variables to macroscopic changes in network topology, and linking major structural transition to phase changes in the thermodynamic picture. We start from a recent quantum-mechanical characterization of the structure of a network relating the graph Laplacian...
In this paper, we use the Maxwell-Boltzmann partition function to compute network entropy. The partition function is used to model the energy level population statistics where the network is in thermodynamic equilibrium with a heat-bath. Here the network Hamiltonian operator defines a set of energy levels occupied by particles in thermal equilibrium. These energy levels are given by the eigenvalues...
In this paper we establish a formal link between network complexity in terms of Birkhoff-von Newmann decompositions and heat flow complexity (in terms of quantifying the heat flowing through the network at a given inverse temperature). Furthermore, we also define heat flow complexity in terms of thermodynamic depth, which results in a novel approach for characterizing networks and quantify their complexity...
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