is_valid_joint_degree#
- is_valid_joint_degree(joint_degrees)[source]#
Checks whether the given joint degree dictionary is realizable.
A joint degree dictionary is a dictionary of dictionaries, in which entry
joint_degrees[k][l]is an integer representing the number of edges joining nodes of degree k with nodes of degree l. Such a dictionary is realizable as a simple graph if and only if the following conditions are satisfied.each entry must be an integer,
the total number of nodes of degree k, computed by
sum(joint_degrees[k].values()) / k, must be an integer,the total number of edges joining nodes of degree k with nodes of degree l cannot exceed the total number of possible edges,
each diagonal entry
joint_degrees[k][k]must be even (this is a convention assumed by thejoint_degree_graph()function).
- Parameters:
- joint_degreesdictionary of dictionary of integers
A joint degree dictionary in which entry
joint_degrees[k][l]is the number of edges joining nodes of degree k with nodes of degree l.
- Returns:
- bool
Whether the given joint degree dictionary is realizable as a simple graph.
References
[1]M. Gjoka, M. Kurant, A. Markopoulou, “2.5K Graphs: from Sampling to Generation”, IEEE Infocom, 2013.
[2]I. Stanton, A. Pinar, “Constructing and sampling graphs with a prescribed joint degree distribution”, Journal of Experimental Algorithmics, 2012.