Tie Length

Structural Meaning

Granovetter introduces a second, structural, meaning. The structural strength of a tie refers to the ability of a tie to facilitate diffusion, cohesion, and integration of a social network by linking otherwise distant nodes. Granovetter's insight is that ties that are weak in the relational sense—that the relations are less salient or frequent—are often strong in the structural sense, in that they are more likely to be formed between socially distant actors with few network “neighbors” in common. Strong social relations have a structural weakness—transitivity, or “triadic closure.” If Adam and Betty are close friends, and Betty and Charlie are close friends, then it is also likely that Adam and Charlie are close friends. Information in closed triads tends to be redundant, which inhibits diffusion. Adam, Betty, and Charlie may strongly influence one another, but if they all know the same things, their close friends will not help them learn about opportunities, developments, or new ideas in socially distant settings.

Simply put, close friends tend to have a high proportion of friends in common; that is, they have high overlap between their networks, and information from friends with high overlap is likely to be redundant. That is the weakness of strong ties.

Weak ties, such as casual friends, have a longer geoedesic range and therefore do not overlap like strong ties.

Conversely, the strength of weak ties is that they have longer range. The range of a tie is the geodesic that it spans (i.e., the shortest distance between two connected [Page 864]nodes if the tie between the nodes were to be removed). These long-range ties between otherwise distant nodes provide access to new information and greatly increase the rate at which information propagates, despite the relational weakness of the tie as a conduit.

Range and overlap measure different dimensions of the contribution of an edge to the spread of novel information. Overlap between two neighbors i and j measures the relative likelihood that i will talk to another neighbor who has also been in direct contact with j. The higher the overlap, the more likely that i will already have heard from a common neighbor the information obtained from j. At zero overlap, adjacent nodes have no shared neighbors, although they might have common neighbors of neighbors. Thus, an edge with zero overlap does not rule out the possibility that i will already have obtained the information from a neighbor of a neighbor of j, or perhaps even from a neighbor of a neighbor of a neighbor, and so on. Range measures how far redundant information from j would have to travel in order to reach i indirectly, via a neighbor of a neighbor, and so on. By definition, overlap will always be zero for any edge with range greater than two, and the range will always be two for any edge with overlap greater than zero. That is, only those edges with minimum range can vary in overlap, and only those edges with minimum overlap can vary in range. Overlap thus allows us to distinguish among edges with minimum range, and range allows us to distinguish among edges with minimum overlap. As a heuristic, one might think of overlap as the “width” of a bridge between network neighborhoods and range as the “length,” where width and length do not vary independently.

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