fiedler_vector¶
- fiedler_vector(G, weight='weight', normalized=False, tol=1e-08, method='tracemin')[source]¶
Return the Fiedler vector of a connected undirected graph.
The Fiedler vector of a connected undirected graph is the eigenvector corresponding to the second smallest eigenvalue of the Laplacian matrix of of the graph.
Parameters: - 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: fiedler_vector – Fiedler vector.
Return type: NumPy array of floats.
Raises : - NetworkXNotImplemented – If G is directed.
- NetworkXError – If G has less than two nodes or is not connected.
Notes
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.
See also
laplacian_matrix()