networkx.linalg.algebraicconnectivity.algebraic_connectivity¶

algebraic_connectivity
(G, weight='weight', normalized=False, tol=1e08, method='tracemin_pcg', seed=None)[source]¶ Return the algebraic connectivity of an undirected graph.
The algebraic connectivity of a connected undirected graph is the second smallest eigenvalue of its Laplacian matrix.
Parameters: G (NetworkX graph) – An undirected graph.
weight (object, optional (default: None)) – The data key used to determine the weight of each edge. If None, then each edge has unit weight.
normalized (bool, optional (default: False)) – Whether the normalized Laplacian matrix is used.
tol (float, optional (default: 1e8)) – Tolerance of relative residual in eigenvalue computation.
method (string, optional (default: ‘tracemin_pcg’)) – Method of eigenvalue computation. It must be one of the tracemin options shown below (TraceMIN), ‘lanczos’ (Lanczos iteration) or ‘lobpcg’ (LOBPCG).
The TraceMIN algorithm uses a linear system solver. The following values allow specifying the solver to be used.
Value Solver ‘tracemin_pcg’ Preconditioned conjugate gradient method ‘tracemin_chol’ Cholesky factorization ‘tracemin_lu’ LU factorization seed (integer, random_state, or None (default)) – Indicator of random number generation state. See Randomness.
Returns: algebraic_connectivity – Algebraic connectivity.
Return type: Raises: NetworkXNotImplemented
– If G is directed.NetworkXError
– If G has less than two nodes.
Notes
Edge weights are interpreted by their absolute values. For MultiGraph’s, weights of parallel edges are summed. Zeroweighted edges are ignored.
To use Cholesky factorization in the TraceMIN algorithm, the
scikits.sparse
package must be installed.See also
laplacian_matrix()