k-core is a notion capturing the cohesiveness of a subgraph in a social network graph. Most of the current research work only consider pure network graphs and neglect an important property of the nodes: influence. Li, Qin, Yu, and Mao introduced a novel community model called k-influential community which is based on the concept of k-core enhanced with node influence values. In this model, we are interested not only in subgraphs that are well-connected but also have a high lower-bound on their influence. More precisely, we are interested in finding top r (with respect to influence), k-core communities. We present novel approaches that provide an impressive scalability in solving the problem for graphs of billions of edges using only a consumer-grade machine. / Graduate