Structural comparisons of networks and model-based detection of small-worldness

In this paper, we consider the problem of assessing the “level of small-worldness” of a graph and of detecting small-worldness features in real networks. After discussing the limitations of classical approaches, based on the computation of network indicators, we propose a new procedure, which involves the comparison of network structures at different “observation scales”. This allows small-world features to be caught, even if “hidden” deeply into the network structure. Applications of the procedure to both simulated and real data show the effectiveness of the proposal, also in distinguishing between different small-world models and in detecting emerging small-worldness in dynamical networks.