Graph theory provides theorems (proved consequences) and algorithms (step-by-step procedures) used to obtain information, such as properties of individual points (popularity, centrality, liaison, or bridge status), of pairs (shortest path between two points) or subgroups (clique-detection, triads), and sub-graphs (blocks of points which are ‘structurally equivalent’ by having the same pattern of links).
Earliest sociological uses include sociometry and clique-detection, and more recently social network, kinship and citation structures, and ‘vacancy chains’ tracing the movement of occupational or housing vacancies through a system. Graph theory has also been extended to treat very large networks and to compare actual network structure with randomly constructed graphs.
"graph theory." A Dictionary of Sociology. . Encyclopedia.com. (October 19, 2018). http://www.encyclopedia.com/social-sciences/dictionaries-thesauruses-pictures-and-press-releases/graph-theory
"graph theory." A Dictionary of Sociology. . Retrieved October 19, 2018 from Encyclopedia.com: http://www.encyclopedia.com/social-sciences/dictionaries-thesauruses-pictures-and-press-releases/graph-theory