According to Wikipedia, a dense graph is a graph in which the number of edges is close to the maximal number of edges. The opposite, a graph with only a few edges, is a sparse graph.
In , an algorithm is designed to find the dense subgraph from the whole graph to find the communities on WWW.
 Dourisboure, Y., Geraci, F., & Pellegrini, M. (2007, May). Extraction and classification of dense communities in the web. In Proceedings of the 16th international conference on World Wide Web (pp. 461-470). ACM.