Most social networks of today are populated with several millions of active users, while the most popular of them accommodate way more than one billion. Analyzing such huge complex networks has become particularly demanding in computational terms. A task of paramount importance for understanding the structure of social networks as well as of many other real-world systems is to identify communities, that is, sets of nodes that are more densely connected to each other than to other nodes of the network. In this paper we propose two algorithms for community detection in networks, by employing the neighborhood overlap metric and appropriate spanning tree computations.