- algebraic_connectivity(G, weight='weight', normalized=False, tol=1e-08, method='tracemin_pcg', seed=None)¶
Returns the algebraic connectivity of an undirected graph.
The algebraic connectivity of a connected undirected graph is the second smallest eigenvalue of its Laplacian matrix.
- GNetworkX graph
An undirected graph.
- weightobject, optional (default: None)
The data key used to determine the weight of each edge. If None, then each edge has unit weight.
- normalizedbool, optional (default: False)
Whether the normalized Laplacian matrix is used.
- tolfloat, optional (default: 1e-8)
Tolerance of relative residual in eigenvalue computation.
- methodstring, 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.
Preconditioned conjugate gradient method
- seedinteger, random_state, or None (default)
Indicator of random number generation state. See Randomness.
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.