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. |  |
| 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. |  |
| In | i holds two inward edges. |  |
| Out | i holds two outward edges. |  |
For each pattern, this is the formula for the clustering coefficient (CC):
ci* = δi* / τi*
where {*}={cycle, middleman, in, out}.
These are the triples for each pattern:
τicyc = diin diout - di↔
where di↔ is the number of bilateral edges between i and its neighbors.
τimid = diindiout - di↔
τiin = diin(diin - 1)
τiout = diout(diout - 1)