libpysal.weights.w_local_cluster

libpysal.weights.w_local_cluster(w)

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.        ]])