A social network consists of a finite set of members. Members i and j are said to be linked if either they are friends or they are "friends of friends," which is shown in an example and then formally defined below.

As an example, here is a social network that has five members A, B, C, D, and E. Friends are any two members that are connected by one line segment. For example, A and B are friends, and C and E are friends. Member A has 3 friends; B, C, and D have one friend each; and E has two friends. Members B and C aren't friends, but they are linked by the sequence of friends BAEC.