Leslie, imagine that betweenness is (loosely) the number of shortest paths between everyone and everyone that pass through a given node, k, weighted inversely by the number of equally short paths between the same pairs. For example, suppose we have the following ties: i -> k, k -> j, i -> p, ?p -> j, and j -> q.

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Then, with normal betweenness, node k will receive a half a point for being along one of the two equally short paths from i to j as well as another half point for being along one of the two shortest paths from i to q. But in 2-step betweenness, k will only receive points for paths of length two. So the path from i to q won’t count, as it is of length of 3.

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The reason for using 2-step betweenness is that for some kinds of social processes, such as brokering, we feel that only direct connections matter. So node k brokers the relationship between its two direct contacts i and j, but may not even be aware of q.? 2-step betweenness is particularly useful as an alternative to Burt’s structural hole measures because they take into account nodes that are not in an ego’s network. For example, k’s network consists only of i and j, not p. Structural hole measures will think that k is in a great position. But they don’t take into account the existence of p, who is also brokering between the exact same two people, and diluting k’s position.

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steve

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