sklearn.neighbors.kneighbors_graph(X, n_neighbors, mode=’connectivity’, metric=’minkowski’, p=2, metric_params=None, include_self=False, n_jobs=1)[source]

Computes the (weighted) graph of k-Neighbors for points in X

Read more in the User Guide.


X : array-like or BallTree, shape = [n_samples, n_features]

Sample data, in the form of a numpy array or a precomputed BallTree.

n_neighbors : int

Number of neighbors for each sample.

mode : {‘connectivity’, ‘distance’}, optional

Type of returned matrix: ‘connectivity’ will return the connectivity matrix with ones and zeros, and ‘distance’ will return the distances between neighbors according to the given metric.

metric : string, default ‘minkowski’

The distance metric used to calculate the k-Neighbors for each sample point. The DistanceMetric class gives a list of available metrics. The default distance is ‘euclidean’ (‘minkowski’ metric with the p param equal to 2.)

p : int, default 2

Power parameter for the Minkowski metric. When p = 1, this is equivalent to using manhattan_distance (l1), and euclidean_distance (l2) for p = 2. For arbitrary p, minkowski_distance (l_p) is used.

metric_params : dict, optional

additional keyword arguments for the metric function.

include_self : bool, default=False.

Whether or not to mark each sample as the first nearest neighbor to itself. If None, then True is used for mode=’connectivity’ and False for mode=’distance’ as this will preserve backwards compatibilty.

n_jobs : int, optional (default = 1)

The number of parallel jobs to run for neighbors search. If -1, then the number of jobs is set to the number of CPU cores.


A : sparse matrix in CSR format, shape = [n_samples, n_samples]

A[i, j] is assigned the weight of edge that connects i to j.


>>> X = [[0], [3], [1]]
>>> from sklearn.neighbors import kneighbors_graph
>>> A = kneighbors_graph(X, 2, mode='connectivity', include_self=True)
>>> A.toarray()
array([[ 1.,  0.,  1.],
       [ 0.,  1.,  1.],
       [ 1.,  0.,  1.]])