Community Detection Based on Modularity and k-Plexes

•We define community seeds and propose a novel community detection method MOKP.•MOKP detects big and small communities by taking advantages of k-plex and modularity.•We further propose an algorithm named IMOKP to improve MOKP in two ways.•We define an index named small community level for measuring small communities.•Our methods perform better than some state-of-the-art algorithms on various networks.