Tensor entropy for uniform hypergraphs

Many real world complex systems can be analyzed through a graph/ network prospective. There are two classical and well-known classes of complex networks, scale-fr ee networks and small world networks, which play a significant role in many domains such as social networks, b iology, cognitive science and signal processing [1, 4, 27, 44]. The human genome is a beautiful example of complex dynamic graph. The genome-wide chromosomal conformation (Hi-C) map represents the spatia l proximity of different parts of genome capturing the genome structure over time [40, 42]. When studying s uch dynamic graphs, one is often required to identify the pattern/couple changes including degree distributio n, path lengths, clustering coefficients, etc, in the graph topology in order to capture the dynamics [25, 33, 41]. The von Neumann entropy of a graph, first introduced by Braunst ein et al. [8], is a spectral measure used in structural pattern recognition. The intuition behind this me asure is linking the graph Laplacian to density matrices from quantum mechanics, and measuring the comp lexity of the graphs in terms of the von Neumman entropy of the corresponding density matrices [32]. In ad dition, the measure can be viewed as the information theoretic Shannon entropy, i.e., S null