is_valid_directed_joint_degree(in_degrees, out_degrees, nkk)[source]

Checks whether the given directed joint degree input is realizable

in_degreeslist of integers

in degree sequence contains the in degrees of nodes.

out_degreeslist of integers

out degree sequence contains the out degrees of nodes.

nkkdictionary of dictionary of integers

directed joint degree dictionary. for nodes of out degree k (first level of dict) and nodes of in degree l (seconnd level of dict) describes the number of edges.


returns true if given input is realizable, else returns false.


Here is the list of conditions that the inputs (in/out degree sequences, nkk) need to satisfy for simple directed graph realizability:

  • Condition 0: in_degrees and out_degrees have the same length

  • Condition 1: nkk[k][l] is integer for all k,l

  • Condition 2: sum(nkk[k])/k = number of nodes with partition id k, is an

    integer and matching degree sequence

  • Condition 3: number of edges and non-chords between k and l cannot exceed

    maximum possible number of edges


[1] B. Tillman, A. Markopoulou, C. T. Butts & M. Gjoka,

“Construction of Directed 2K Graphs”. In Proc. of KDD 2017.