hiperwalk.WeightedGraph

class hiperwalk.WeightedGraph(adj_matrix, copy=False)

Construct an arbitrary weighted graph.

This class enables the creation of a weighted graph, defined by a Hermitian adjacency matrix that represents the connections between nodes and edge weights.

Parameters:

adj_matrixvarious types accepted

The adjacency matrix of the graph, which must be a Hermitian matrix. Two types of input are accepted:

• Matrix formats such as:

  • scipy.sparse.csr_array,

  • numpy.ndarray,

  • List of lists.

• networkx.Graph:

  The adjacency matrix is derived from the provided NetworkX graph.

copybool, default=False

Determines how the adjacency matrix is stored:

• If True, a deep copy of adj_matrix is created and stored.

• If False, a reference to the original adj_matrix is stored.

Raises:

TypeError

If adj_matrix is not a square matrix, indicating it cannot represent a valid adjacency matrix.

Notes

When defining an instance of the Coined class on a weighted graph, the edge weights do not affect the simulation.

When defining an instance of the ContinuousTime class on a weighted graph, the edge weights do affect the simulation.

__init__(adj_matrix, copy=False)

Methods

adjacency_matrix([copy])	Return the adjacency matrix representation of the graph.
adjacent(u, v)	Return True if vertex u is adjacent to v.
degree(vertex)	Return the degree of the given vertex.
is_simple()	Return True if the graph has no multiedges or weights.
laplacian_matrix()	Return the graph's Laplacian matrix.
neighbors(vertex)	Return all neighbors of the given vertex.
number_of_edges()	Return the total number of edges in the graph.
number_of_loops()	Return the number of loops in the graph.
number_of_vertices()	Return the total number of vertices in the graph.
vertex_number(vertex)	Return the numerical label of a vertex based on its representation.