method. Harary made many unique contributions to graph theory as he explored more and more different fields of study and successfully attempted to relate them to graph theory. Harary's classic book Graph Theory begins by providing the reader with much of the requisite knowledge of basic graphs and then dives right into proving the diversity of content that is held within graph theory. Some of the other mathematical fields that Harary directly relates to graph theory in his book begin to appear around chapter 13, these topics include linear algebra, and abstract algebra. Harary also made an influential contribution in the theory of social learning used in sociology and behavioral economics, deriving a criterion for consensus in John R. P. French's model of social power. This anticipated by several decades, albeit in a special case, the widely used DeGroot learning model. Tree square root One motivation for the study of graph theory is its application to sociograms described by Jacob L. Moreno. For instance the adjacency matrix of a sociogram was used by Leon Festinger. Festinger identified the graph theory clique with the social clique and examined the diagonal of the cube of a groups’ adjacency matrix to detect cliques. Harary joined with Ian Ross to improve on Festinger's clique detection. The admission of powers of an adjacency matrix led Harary and Ross to note that a complete graph can be obtained from the square of an adjacency matrix of a tree. Relying on their study of clique detection, they described a class of graphs for which the adjacency matrix is the square of the adjacency matrix of a tree. If a graph G is the square of a tree, then it has a unique tree square root Some vocabulary necessary to understand this proof and the methods used here are provided in Harary's The Square of a Tree: (Cliqual, unicliqual, multicliqual, cocliqual, neighborhood, neighborly, cut point, block) How to determine if some graph G is the square of a tree. Iff a graph G is complete or satisfies the following 5 properties then G = T2 (i) Every point of G is neighborly and G is connected. (ii) If two cliques meet at only one point b, then there is a third clique with which they share b and exactly one other point. (iii) There is a 1-1 correspondence between the cliques and the multicliqual points b of G