### Abstract

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

Article number | 083052 |

Journal | New Journal of Physics |

Volume | 17 |

DOIs | |

Publication status | Published - 31 Aug 2015 |

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### Bibliographical note

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.

### Cite this

*New Journal of Physics*,

*17*, [083052]. https://doi.org/10.1088/1367-2630/17/8/083052

**Exact sampling of graphs with prescribed degree correlations.** / Bassler, Kevin; del Genio, Charo; Erdős, Peter; Miklós, Istvan; Toroczkai, Zoltán.

Research output: Contribution to journal › Article

*New Journal of Physics*, vol. 17, 083052. https://doi.org/10.1088/1367-2630/17/8/083052

}

TY - JOUR

T1 - Exact sampling of graphs with prescribed degree correlations

AU - Bassler, Kevin

AU - del Genio, Charo

AU - Erdős, Peter

AU - Miklós, Istvan

AU - Toroczkai, Zoltán

N1 - Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.

PY - 2015/8/31

Y1 - 2015/8/31

N2 - Many real-world networks exhibit correlations between the node degrees. For instance, in social networks nodes tend to connect to nodes of similar degree. Conversely, in biological and technological networks, high-degree nodes tend to be linked with low-degree nodes. Degree correlations also affect the dynamics of processes supported by a network structure, such as the spread of opinions or epidemics. The proper modelling of these systems, i.e., without uncontrolled biases, requires the sampling of networks with a specified set of constraints. We present a solution to the sampling problem when the constraints imposed are the degree correlations. In particular, we develop an efficient and exact method to construct and sample graphs with a specified joint-degree matrix, which is a matrix providing the number of edges between all the sets of nodes of a given degree, for all degrees, thus completely specifying all pairwise degree correlations, and additionally, the degree sequence itself. Our algorithm always produces independent samples without backtracking. The complexity of the graph construction algorithm is O(NM) where N is the number of nodes and M is the number of edges.

AB - Many real-world networks exhibit correlations between the node degrees. For instance, in social networks nodes tend to connect to nodes of similar degree. Conversely, in biological and technological networks, high-degree nodes tend to be linked with low-degree nodes. Degree correlations also affect the dynamics of processes supported by a network structure, such as the spread of opinions or epidemics. The proper modelling of these systems, i.e., without uncontrolled biases, requires the sampling of networks with a specified set of constraints. We present a solution to the sampling problem when the constraints imposed are the degree correlations. In particular, we develop an efficient and exact method to construct and sample graphs with a specified joint-degree matrix, which is a matrix providing the number of edges between all the sets of nodes of a given degree, for all degrees, thus completely specifying all pairwise degree correlations, and additionally, the degree sequence itself. Our algorithm always produces independent samples without backtracking. The complexity of the graph construction algorithm is O(NM) where N is the number of nodes and M is the number of edges.

UR - https://charodelgenio.weebly.com/sampling-graphs-with-given-correlations.html

U2 - 10.1088/1367-2630/17/8/083052

DO - 10.1088/1367-2630/17/8/083052

M3 - Article

VL - 17

JO - New Journal of Physics

JF - New Journal of Physics

M1 - 083052

ER -