For an unweighted, directed network (BDN), given a vertex i, the BDN triangle types can be categorized to four patterns.
| Pattern | Description | Illustration |
|---|---|---|
| Cycle | There is a cyclical relation among i and any two of its neighbors: i→j→h→i, or the reverse. |
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| Middleman | One of i’s neighbors, j, both holds an outward edge to a third neighbor, h, and uses i to reach h in two steps. |
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| In | i holds two inward edges. |
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| Out | i holds two outward edges. |
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For each pattern, this is the formula for the clustering coefficient (CC):
c i * = δ i * / τ i *
where {*}={cycle, middleman, in, out}.
These are the triples for each pattern:
τ i cyc = d i in d i out - d i ↔
where d i ↔ is the number of bilateral edges between i and its neighbors.
τ i mid = d i in d i out - d i ↔
τ i in = d i in (d i in - 1)
τ i out = d i out (d i out - 1)