There has been significant interest in the study of the problem of community search in large networks. Given one or more query nodes, this problem aims to discover densely connected subgroups containing these nodes. Various algorithms have been proposed to solve this challenging problem using different measures or a variety of cohesive subgraphs. In this paper, given an undirected graph and a set of query nodes, we study the community search using novel several cohesive subgraph models. More precisely, we propose to exploit several cohesive structures in a unified framework to find densely communities for query nodes in large complex networks. First, we review some existing cohesive structures. Next, to make these structures more effective models of communities, we focus on interesting configurations that are larger and more cohesive by fulfilling some constraints. The new structures obtained allow to ensure a larger density on the discovered communities and overcome some weaknesses of existing models. Finally, empirical results show the effectiveness of our framework to find communities for query nodes in a variety of real graphs.