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- algebraic_connectivity(G, weight='weight', normalized=False, tol=1e-08, method='tracemin')¶
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.
G : NetworkX graph
An undirected graph.
weight : object, optional
The data key used to determine the weight of each edge. If None, then each edge has unit weight. Default value: None.
normalized : bool, optional
Whether the normalized Laplacian matrix is used. Default value: False.
tol : float, optional
Tolerance of relative residual in eigenvalue computation. Default value: 1e-8.
method : string, optional
Method of eigenvalue computation. It should be one of ‘tracemin’ (TraceMIN), ‘lanczos’ (Lanczos iteration) and ‘lobpcg’ (LOBPCG). Default value: ‘tracemin’.
The TraceMIN algorithm uses a linear system solver. The following values allow specifying the solver to be used.
Preconditioned conjugate gradient method
algebraic_connectivity : float
If G is directed.
If G has less than two nodes.
Edge weights are interpreted by their absolute values. For MultiGraph’s, weights of parallel edges are summed. Zero-weighted edges are ignored.
To use Cholesky factorization in the TraceMIN algorithm, the scikits.sparse package must be installed.