### Abstract

Functional networks of complex systems are obtained from the analysis of the temporal activity of their components, and are often used to infer their unknown underlying connectivity. We obtain the equations relating topology and function in a system of diffusively delay-coupled elements in complex networks. We solve exactly the resulting equations in motifs (directed structures of three nodes) and in directed networks. The mean-field solution for directed uncorrelated networks shows that the clusterization of the activity is dominated by the in-degree of the nodes, and that the locking frequency decreases with increasing average degree. We find that the exponent of a power law degree distribution of the structural topology γ is related to the exponent of the associated functional network as α=(2-γ)^{-}1 for γ<2.

Original language | English |
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Article number | 056113 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 83 |

Issue number | 5 |

DOIs | |

Publication status | Published - 19 May 2011 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Statistics and Probability

### Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*83*(5), [056113]. https://doi.org/10.1103/PhysRevE.83.056113

**Structural and functional networks in complex systems with delay.** / Eguíluz, Víctor M.; Pérez, Toni; Borge-Holthoefer, Javier; Arenas, Alex.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 83, no. 5, 056113. https://doi.org/10.1103/PhysRevE.83.056113

}

TY - JOUR

T1 - Structural and functional networks in complex systems with delay

AU - Eguíluz, Víctor M.

AU - Pérez, Toni

AU - Borge-Holthoefer, Javier

AU - Arenas, Alex

PY - 2011/5/19

Y1 - 2011/5/19

N2 - Functional networks of complex systems are obtained from the analysis of the temporal activity of their components, and are often used to infer their unknown underlying connectivity. We obtain the equations relating topology and function in a system of diffusively delay-coupled elements in complex networks. We solve exactly the resulting equations in motifs (directed structures of three nodes) and in directed networks. The mean-field solution for directed uncorrelated networks shows that the clusterization of the activity is dominated by the in-degree of the nodes, and that the locking frequency decreases with increasing average degree. We find that the exponent of a power law degree distribution of the structural topology γ is related to the exponent of the associated functional network as α=(2-γ)-1 for γ<2.

AB - Functional networks of complex systems are obtained from the analysis of the temporal activity of their components, and are often used to infer their unknown underlying connectivity. We obtain the equations relating topology and function in a system of diffusively delay-coupled elements in complex networks. We solve exactly the resulting equations in motifs (directed structures of three nodes) and in directed networks. The mean-field solution for directed uncorrelated networks shows that the clusterization of the activity is dominated by the in-degree of the nodes, and that the locking frequency decreases with increasing average degree. We find that the exponent of a power law degree distribution of the structural topology γ is related to the exponent of the associated functional network as α=(2-γ)-1 for γ<2.

UR - http://www.scopus.com/inward/record.url?scp=84876808970&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84876808970&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.83.056113

DO - 10.1103/PhysRevE.83.056113

M3 - Article

C2 - 21728611

AN - SCOPUS:84876808970

VL - 83

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 5

M1 - 056113

ER -