Degree-based graph construction

Hyunju Kim, Zoltn Toroczkai, Péter L. Erds, I. Miklós, Lszló A. Székely

Research output: Contribution to journalArticle

33 Citations (Scopus)

Abstract

Degree-based graph construction is a ubiquitous problem in network modelling (Newman et al 2006 The Structure and Dynamics of Networks (Princeton Studies in Complexity) (Princeton, NJ: Princeton University Press), Boccaletti et al 2006 Phys. Rep. 424 175), ranging from social sciences to chemical compounds and biochemical reaction networks in the cell. This problem includes existence, enumeration, exhaustive construction and sampling questions with aspects that are still open today. Here we give necessary and sufficient conditions for a sequence of nonnegative integers to be realized as a simple graph's degree sequence, such that a given (but otherwise arbitrary) set of connections from an arbitrarily given node is avoided. We then use this result to present a swap-free algorithm that builds all simple graphs realizing a given degree sequence. In a wider context, we show that our result provides a greedy construction method to build all the f-factor subgraphs (Tutte 1952 Can. J. Math. 4 314) embedded within Kn Sk, where Kn is the complete graph and Sk is a star graph centred on one of the nodes.

Original languageEnglish
Article number392001
JournalJournal of Physics A: Mathematical and Theoretical
Volume42
Issue number39
DOIs
Publication statusPublished - 2009

Fingerprint

Degree Sequence
Simple Graph
Graph in graph theory
Star Graph
Biochemical Networks
Reaction Network
chemical compounds
enumeration
Chemical compounds
Social sciences
Network Modeling
Swap
Social Sciences
Vertex of a graph
Complete Graph
Enumeration
Stars
integers
Subgraph
Non-negative

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Modelling and Simulation
  • Statistics and Probability

Cite this

Degree-based graph construction. / Kim, Hyunju; Toroczkai, Zoltn; Erds, Péter L.; Miklós, I.; Székely, Lszló A.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 42, No. 39, 392001, 2009.

Research output: Contribution to journalArticle

Kim, Hyunju ; Toroczkai, Zoltn ; Erds, Péter L. ; Miklós, I. ; Székely, Lszló A. / Degree-based graph construction. In: Journal of Physics A: Mathematical and Theoretical. 2009 ; Vol. 42, No. 39.
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