Studies of social structures has been grown on the last years, because its sharing form and content creation attracted the public in general. Such structures are observed, as an example, in literary pieces. A featured author is J.R.R. Tolkien, with his books that describe a fictional world and its inhabitants. These books bring a narrative of the creation of the Middle-Earth and all of its mythology. His main pieces are: The Silmarillion, The Hobbit and The Lord of the rings, The objective of this article is the analysis of the social structures emerging of the conjunction of these works, where the social relations are described by the reference criteria, shared events and direct bonds, with the major centrality measures together with the structural entropy of first order. Enabling the doing of an analogy with the canonic ensemble of the mechanics statistics and enabling analyzing the degree of homogeneity of the bonds between the formed communities.