Statistical fidelity: a tool to quantify the similarity between multi-variable entities with application in complex networks.

Complex networks are often characterized by their underlying graph metrics, yet there is no unified computational method for comparing networks to each other. Given that complex networks are entities characterized by a set of known properties, our problem is reduced to quantifying the similarity between the multi-variable entities. To address this issue, we introduce the new statistical fidelity metric, which can compare any types of entities, characterized by specific individual metrics, in order to gauge the similarity of the entities under the form of a single number between 0 and 1. To test the efficiency of statistical fidelity, we apply our composite metric in the field of complex networks, by assessing topological similarity and realism of social networks and urban road networks. Pinned against other statistical methods, such as the cosine similarity, Pearson correlation, Mahalanobis distance and fractal dimension, we highlight the superior analytic power of statistical fidelity.