### 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 K_{n} S_{k}, where K_{n} is the complete graph and S_{k} is a star graph centred on one of the nodes.

Original language | English |
---|---|

Article number | 392001 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 42 |

Issue number | 39 |

DOIs | |

Publication status | Published - 2009 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*42*(39), [392001]. https://doi.org/10.1088/1751-8113/42/39/392001

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

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 42, no. 39, 392001. https://doi.org/10.1088/1751-8113/42/39/392001

}

TY - JOUR

T1 - Degree-based graph construction

AU - Kim, Hyunju

AU - Toroczkai, Zoltn

AU - Erds, Péter L.

AU - Miklós, I.

AU - Székely, Lszló A.

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=70449494651&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70449494651&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/42/39/392001

DO - 10.1088/1751-8113/42/39/392001

M3 - Article

VL - 42

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 39

M1 - 392001

ER -