Advanced graph mining for community evaluation in social networks and the web

Graphs constitute a dominant data structure and appear essentially in all forms of information. Examples are the Web graph, numerous social networks, protein interaction networks, terms dependency graphs and network topologies. The main features of these graphs are their huge volume and rate of change. Presumably, there is important hidden knowledge in the macroscopic topology and features of these graphs. A cornerstone issue here is the detection and evaluation of communities -- bearing multiple and diverse semantics. The tutorial reports the basic models of graph structures for undirected, directed and signed graphs and their properties. Next we offer a thorough review of fundamental methods for graph clustering and community detection, on both undirected and directed graphs. Then we survey community evaluation measures, including both the individual node based ones as well as those that take into account aggregate properties of communities. A special mention is made on approaches that capitalize on the concept of degeneracy (k-cores and extensions), as a novel means of community detection and evaluation. We justify the above foundational framework with applications on citation graphs, trust networks and protein graphs.