# libpysal.weights.w_local_cluster¶

libpysal.weights.w_local_cluster(w)[source]

Local clustering coefficients for each unit as a node in a graph.

Parameters
wW

spatial weights object

Returns
carray

(w.n,1) local clustering coefficients

Notes

The local clustering coefficient $$c_i$$ quantifies how close the neighbors of observation $$i$$ are to being a clique:

$c_i = | \{w_{j,k}\} |/ (k_i(k_i - 1)): j,k \in N_i$

where $$N_i$$ is the set of neighbors to $$i$$, $$k_i = |N_i|$$ and $$\{w_{j,k}\}$$ is the set of non-zero elements of the weights between pairs in $$N_i$$ [WS98].

Examples

>>> from libpysal.weights import lat2W, w_local_cluster
>>> w = lat2W(3,3, rook=False)
>>> w_local_cluster(w)
array([[1.        ],
[0.6       ],
[1.        ],
[0.6       ],
[0.42857143],
[0.6       ],
[1.        ],
[0.6       ],
[1.        ]])