This documents an unmaintained version of NetworkX. Please upgrade to a maintained version and see the current NetworkX documentation.
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.
Value Solver ‘tracemin_pcg’ Preconditioned conjugate gradient method ‘tracemin_chol’ Cholesky factorization ‘tracemin_lu’ LU factorization Returns:
algebraic_connectivity – Algebraic connectivity.
Return type: Raises:
NetworkXNotImplemented– If G is directed.
NetworkXError– 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.sparsepackage must be installed.