### Abstract

Many real-world networks exhibit correlations between the node degrees. For instance, in socialnetworks nodes tend to connect to nodes of similar degree and 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.Wepresent a solution to the sampling problem when the constraints imposed are the degree correlations. In particular, we develop an 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 algorithmis ⊙(NM)whereNis the number of nodes andMis the number of edges.

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

Article number | 083052 |

Journal | New Journal of Physics |

Volume | 17 |

Issue number | 8 |

DOIs | |

Publication status | Published - Aug 26 2015 |

### Fingerprint

### Keywords

- algorithm
- complex networks
- correlations
- joint-degree matrix
- sampling

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*New Journal of Physics*,

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

**Exact sampling of graphs with prescribed degree correlations.** / Bassler, Kevin E.; Genio, Charo I Del; Erds, Péter L.; Miklós, I.; Toroczkai, Zoltán.

Research output: Contribution to journal › Article

*New Journal of Physics*, vol. 17, no. 8, 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 E.

AU - Genio, Charo I Del

AU - Erds, Péter L.

AU - Miklós, I.

AU - Toroczkai, Zoltán

PY - 2015/8/26

Y1 - 2015/8/26

N2 - Many real-world networks exhibit correlations between the node degrees. For instance, in socialnetworks nodes tend to connect to nodes of similar degree and 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.Wepresent a solution to the sampling problem when the constraints imposed are the degree correlations. In particular, we develop an 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 algorithmis ⊙(NM)whereNis the number of nodes andMis the number of edges.

AB - Many real-world networks exhibit correlations between the node degrees. For instance, in socialnetworks nodes tend to connect to nodes of similar degree and 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.Wepresent a solution to the sampling problem when the constraints imposed are the degree correlations. In particular, we develop an 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 algorithmis ⊙(NM)whereNis the number of nodes andMis the number of edges.

KW - algorithm

KW - complex networks

KW - correlations

KW - joint-degree matrix

KW - sampling

UR - http://www.scopus.com/inward/record.url?scp=84941662074&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84941662074&partnerID=8YFLogxK

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

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

M3 - Article

AN - SCOPUS:84941662074

VL - 17

JO - New Journal of Physics

JF - New Journal of Physics

SN - 1367-2630

IS - 8

M1 - 083052

ER -