networkx.generators.joint_degree_seq.is_valid_joint_degree¶

is_valid_joint_degree
(joint_degrees)[source]¶ Checks whether the given joint degree dictionary is realizable as a simple graph.
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_degrees (dictionary 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: Whether the given joint degree dictionary is realizable as a simple graph. Return type: bool 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.