One reason for using mathematical and graphical techniques in social network analysis is to represent the descriptions of networks compactly and systematically. This also enables us to use computers to store and manipulate the information quickly and more accurately than we can by hand. For small populations of actors (e.g. the people in a neighborhood, or the business firms in an industry), we can describe the pattern of social relationships that connect the actors rather completely and effectively using words. To make sure that our description is complete, however, we might want to list all logically possible pairs of actors, and describe each kind of possible relationship for each pair. This can get pretty tedious if the number of actors and/or number of kinds of relations is large. Formal representations ensure that all the necessary information is systematically represented, and provides rules for doing so in ways that are much more efficient than lists.