Ties, Weak and Strong

The members of every community can be thought of as linked by a network of one-to-one ties between people who are related to one another as friends, neighbors, relatives, or coworkers. The distance between any two people is the minimum number of steps through ties in the network needed to go from one to the other. A common and unusual characteristic of communities is that these distances are not very great, no matter how large the community. This would not be surprising if ties were scattered randomly, which they are not. Instead, one-to-one ties in a community tend, often very strongly, to cluster. The strongest kind of cluster is the clique, in which everyone has a tie to everyone else. If everyone’s ties are strictly embedded in cliques then each pair of each person’s partners (ego to A and B) are themselves partners (A and B): This would exclude the possibility of bridges between cliques, which are ties that connect cliques but are not part of a clique. What would we find if a clustering index of the transitivity of such triples were done for each person in a network? That is, if A likes B and C, how often do B and C like each other? If the index were perfectly transitive for everyone, then people in different cliques are required to be disconnected and the distances between them would be infinite.