Quantum-inspired measures of network distinguishability

The recent emergence of information physics as a theoretical foundation for complex networks has inspired the utilization of measures, initially developed for use with quantum mechanical systems, for the solution of graph theory research problems. Network comparison is one such research problem that arises often in all domains, when entities that interact with each other possibly with more than one discrete interaction types are studied. A network similarity measure is required for any data mining application on graphs, such as graph clustering, classification, or outlier detection. A natural starting point for the identification of such a network similarity measure is information physics, offering a series of measures typically used to quantify the distance of quantum states. These quantum-inspired methods satisfy the mathematical requirements for graph similarity while offering high interpretability. In this work, we characterize these measures for use with monoplex and multiplex networks on experiments with synthetic data, and we report results on real-world applications to compare with a series of state-of-the-art and well-established methods of graph distinguishability.