Degree-preserving network growth

Degree-preserving graph dynamics -- a versatile process to construct random networks

“…When the graph is dense and there are not many low degree nodes, [17] (in the Supplementary Information) provides a tighter bound on the matching number, based on Theorem 3.2. Definition 3.3.…”

“…As demonstrated in [17], the DPG process can also be used to generate real-world like synthetic scale-free networks in such a way that the process does not inherently prefer any node over another, and the degrees of already inserted nodes do not change. Moreover, simulations showed [17] that the generated degree sequences are indeed scalefree with the desired exponent. In this section we discuss the protocol in detail and prove that the generated degree sequence belongs to the set of power-law distributionbounded degree sequences.…”

“…In Ref. [17], tens of real-world networks were studied, if whether they can be constructed from small initial "kernel" graphs via the DPG-process. Note that there can be many DP paths leading to the same target graph, starting from different small kernel graphs or possibly even from the same small kernel graph.…”

“…In this paper we will also discuss new results on different DPG models (see Section 3) as well as some extensions of the algorithmic and stochastic considerations of DPG processes defined in Ref. [17].…”

“…(Instead of proving this statement directly, we will prove a generalization of Theorem 3.6 in the following Theorem 3.7.) The edge density of G n is ρ n = 1 2 − O ln n n , and one can show [17] that it has a core-periphery structure. More precisely, it resembles a split graph in which the nodes are partitioned into three classes: one inducing a clique in G n , another is an independent set, and the third set contains at most O(log 2 n) vertices.…”