How can we approximate sparse graphs and sequences of (with unbounded average degree)? We consider convergence in the first k moments graph spectrum (equivalent to numbers closed -walks) appropriately normalized. introduce a simple random model that captures limiting spectra many interest, including sequence hypercube graphs. The overlapping communities (ROC) is specified by distribution on pai...

Networks provide a powerful way to study complex systems of interacting objects. Detecting network communities—groups of objects that often correspond to functional modules—is crucial to understanding social, technological, and biological systems. Revealing communities allows for analysis of system properties that are invisible when considering only individual objects or the entire system, such...

Community structure is the key aspect of complex network analysis and it has important practical significance. While in real networks, some nodes may belong to multiple communities, so overlapping community detection attracts more and more attention. But most of the existing overlapping community detection algorithms increase the time complexity in some extent. In order to detect overlapping co...