Distance entropy cartography characterises centrality in complex networks

We introduce distance entropy as a measure of homogeneity in the distribution of path lengths between a given node and its neighbours in a complex network. Distance entropy defines a new centrality measure whose properties are investigated for a variety of synthetic network models. By coupling distance entropy information with closeness centrality, we introduce a network cartography which allows one to reduce the degeneracy of ranking based on closeness alone. We apply this methodology to the empirical multiplex lexical network encoding the linguistic relationships known to English speaking toddlers. We show that the distance entropy cartography better predicts how children learn words compared to closeness centrality. Our results highlight the importance of distance entropy for gaining insights from distance patterns in complex networks.Comment: 11 page

Local Ranking Problem on the BrowseGraph

The "Local Ranking Problem" (LRP) is related to the computation of a centrality-like rank on a local graph, where the scores of the nodes could significantly differ from the ones computed on the global graph. Previous work has studied LRP on the hyperlink graph but never on the BrowseGraph, namely a graph where nodes are webpages and edges are browsing transitions. Recently, this graph has received more and more attention in many different tasks such as ranking, prediction and recommendation. However, a web-server has only the browsing traffic performed on its pages (local BrowseGraph) and, as a consequence, the local computation can lead to estimation errors, which hinders the increasing number of applications in the state of the art. Also, although the divergence between the local and global ranks has been measured, the possibility of estimating such divergence using only local knowledge has been mainly overlooked. These aspects are of great interest for online service providers who want to: (i) gauge their ability to correctly assess the importance of their resources only based on their local knowledge, and (ii) take into account real user browsing fluxes that better capture the actual user interest than the static hyperlink network. We study the LRP problem on a BrowseGraph from a large news provider, considering as subgraphs the aggregations of browsing traces of users coming from different domains. We show that the distance between rankings can be accurately predicted based only on structural information of the local graph, being able to achieve an average rank correlation as high as 0.8