ott.geometry.geodesic.Geodesic.from_graph#
- classmethod Geodesic.from_graph(G, t=0.001, eigval=None, order=100, directed=False, normalize=False, rng=None, **kwargs)[source]#
Construct a Geodesic geometry from an adjacency matrix.
- Parameters:
t (
Optional
[float
]) – Time parameter for approximating the geodesic exponential kernel. If None, it defaults to \(\frac{1}{|E|} \sum_{(u, v) \in E} \text{weight}(u, v)\) [Crane et al., 2013]. In this case, thegraph
must be specified and the edge weights are assumed to be positive.eigval (
Optional
[Array
]) – Largest eigenvalue of the Laplacian. IfNone
, it’s computed usingjax.experimental.sparse.linalg.lobpcg_standard()
.order (
int
) – Max order of Chebyshev polynomials.directed (
bool
) – Whether thegraph
is directed. IfTrue
, it’s made undirected as \(G + G^T\). This parameter is ignored when passing the Laplacian directly, assumed to be symmetric.normalize (
bool
) – Whether to normalize the Laplacian as \(L^{sym} = \left(D^+\right)^{\frac{1}{2}} L \left(D^+\right)^{\frac{1}{2}}\), where \(L\) is the non-normalized Laplacian and \(D\) is the degree matrix.rng (
Optional
[Array
]) – Random key used when computing the largest eigenvalue.
- Return type:
- Returns:
The Geodesic geometry.