User-centered analysis is one of the aims of online community search. In this paper, we study personalized top-n influential community search that has a practical application. Given an evolving social network, where every edge has a propagation probability, we propose a maximal pk-Clique community model, that uses a new cohesive criterion. The criterion requires that the propagation probability of each edge or each maximal influence path between two vertices that is considered as an edge, is greater than p. The maximal clique problem is an NP-hard problem, and the introduction of this cohesive criterion makes things worse, as it may add new edges to existing networks. To conduct personalized top-n influential community search efficiently in such networks, we first introduce a search space refinement method. We then present pruning based and heuristic based search approaches. The proposed algorithms more than double the efficiency of the search performance for basic solutions. The effectiveness and efficiency of our algorithms have been verified using four real datasets.