Search in weighted complex networks

We study trade-offs presented by local search algorithms in complex networks which are heterogeneous in edge weights and node degree. We show that search based on a network measure, local betweenness centrality (LBC), utilizes the heterogeneity of both node degrees and edge weights to perform the best in scale-free weighted networks. The search based on LBC is universal and performs well in a large class of complex networks.Comment: 14 pages, 5 figures, 4 tables, minor changes, added a referenc

Analysis of a large-scale weighted network of one-to-one human communication

We construct a connected network of 3.9 million nodes from mobile phone call records, which can be regarded as a proxy for the underlying human communication network at the societal level. We assign two weights on each edge to reflect the strength of social interaction, which are the aggregate call duration and the cumulative number of calls placed between the individuals over a period of 18 weeks. We present a detailed analysis of this weighted network by examining its degree, strength, and weight distributions, as well as its topological assortativity and weighted assortativity, clustering and weighted clustering, together with correlations between these quantities. We give an account of motif intensity and coherence distributions and compare them to a randomized reference system. We also use the concept of link overlap to measure the number of common neighbors any two adjacent nodes have, which serves as a useful local measure for identifying the interconnectedness of communities. We report a positive correlation between the overlap and weight of a link, thus providing strong quantitative evidence for the weak ties hypothesis, a central concept in social network analysis. The percolation properties of the network are found to depend on the type and order of removed links, and they can help understand how the local structure of the network manifests itself at the global level. We hope that our results will contribute to modeling weighted large-scale social networks, and believe that the systematic approach followed here can be adopted to study other weighted networks.Comment: 25 pages, 17 figures, 2 table

Self-organized Emergence of Navigability on Small-World Networks

This paper mainly investigates why small-world networks are navigable and how to navigate small-world networks. We find that the navigability can naturally emerge from self-organization in the absence of prior knowledge about underlying reference frames of networks. Through a process of information exchange and accumulation on networks, a hidden metric space for navigation on networks is constructed. Navigation based on distances between vertices in the hidden metric space can efficiently deliver messages on small-world networks, in which long range connections play an important role. Numerical simulations further suggest that high cluster coefficient and low diameter are both necessary for navigability. These interesting results provide profound insights into scalable routing on the Internet due to its distributed and localized requirements.Comment: 3 figure