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

Abstract

Real-world networks evolve over time via additions or removals of nodes and edges. In current network evolution models, node degree varies or grows arbitrarily. A recently introduced degree-preserving network growth (DPG) family of models preserves node degree, resulting in structures significantly different from and more diverse than previous models ([Nature Physics 2021,

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“…Recently, a new network growth dynamics has been introduced: the degreepreserving network growth (DPG) model family (see [8] or [16]). The DPG-process can be described as follows: let G be a simple graph with degree sequence D. In what follows, by a matching we mean a set of independent edges in the graph, that is, a set of pairwise non-adjacent edges.…”

The sequence of prime gaps is graphic

“…Recently, a new network growth dynamics has been introduced: the degree-preserving network growth (DPG) model family (see [7] or [15]). The DPG process can be described as follows: let G be a simple graph with degree sequence D. In a general step, a new vertex u joins the graph by removing a νelement matching of G followed by connecting u to the vertices incident to the ν removed edges.…”