Graphs

Classes

There are three classes of graph.

Graph	Constructs an arbitrary graph.
Multigraph	Construct an arbitrary multigraph.
WeightedGraph	Construct an arbitrary weighted graph.

hiperwalk.Multigraph is used as input for the hiperwalk.Coined quantum walk model. hiperwalk.WeightedGraph is used as input for the hiperwalk.ContinuousTime quantum walk model. hiperwalk.Graph is used as input for both quantum walk models.

Graph Constructors

The graph constructors [1] return an instance of commonly used graphs.

The graph constructors are used to change the default behavior of specific graphs. For instance, the order of the neighbors changes depending on the graph.

Every constructor has the following template:

>>> GraphConstructor(args, multiedges=None, weights=None) 

where multiedges and weights are optional arguments whose default value is None. Every graph constructor returns an instance of

• hiperwalk.Graph if multiedges is None and weights is None.

• hiperwalk.Multigraph if multiedges is not None and weights is None.

• hiperwalk.WeightedGraph if multiedges is None and weights is not None.

Both multiedges and weights are expected to be instances of dict or scipy.sparse.csr_array.

• If they are an instance of dict in the {(u, v): value} format.

  • multiedges[(u, v)] is the number of edges incident to both vertices u and v.

  • weights[(u, v)] is the weight of the edge incident to both vertices u and v.

  If an edge exists in the graph but it is not listed in the dict keys, its value defaults to 1. Attempting to remove an edge by assigning its value to 0 (e.g. weights[(u, v)] = 0) or attempting to add an edge by assigning a value to it (e.g. weights[(-1, -1) = 10]) raises a a ValueError exception.

• If they are an instance of scipy.sparse.csr_array,

  • multiedges[u, v] is the number of edges incident to both vertices u and v.

  • weights[u, v] is the weight of the edge incident to both vertices u and v.

  In this case, all valid edges must have been assigned a value different from 0. When explicitly specifying the adjacency matrix, the copy changes the method’s behavior.

  • If copy = False (default), a pointer to the adjacency matrix is stored.

  • If copy = True, a hard copy of the adjacency matrix is stored.

If multiedges is not None and weights is not None, a ValueError exception is raised.

[1]

NetworkX uses graph generators for the same concept. However, both constructor and generator are words that already have consolidated meanings. Thus, we decided to use the word constructor because it conveys the idea that an instance is going to be returned.

List of Graph Constructors

The following is the list of all available graph constructors.

• hiperwalk.Complete
• hiperwalk.CompleteBipartite
• hiperwalk.Cycle
• hiperwalk.Grid
• hiperwalk.Hypercube
• hiperwalk.IntegerLattice
• hiperwalk.Line