### Abstract

Confining an answer to the question of whether and how the coherent operation of network elements is determined by the network structure is the topic of our work. We map the structure of signal flow in directed networks by analysing the degree of edge convergence and the overlap between the in-and output sets of an edge. Definitions of convergence degree and overlap are based on the shortest paths, thus they encapsulate global network properties. Using the defining notions of convergence degree and overlapping set we clarify the meaning of network causality and demonstrate the crucial role of chordless circles. In real-world networks the flow representation distinguishes nodes according to their signal transmitting, processing and control properties. The analysis of real-world networks in terms of flow representation was in accordance with the known functional properties of the network nodes. It is shown that nodes with different signal processing, transmitting and control properties are randomly connected at the global scale, while local connectivity patterns depart from randomness. The grouping of network nodes according to their signal flow properties was unrelated to the network's community structure. We present evidence that the signal flow properties of small-world-like, real-world networks cannot be reconstructed by algorithms used to generate small-world networks. Convergence degree values were calculated for regular oriented trees, and the probability density function for networks grown with the preferential attachment mechanism. For Erdos-Rényi graphs we calculated the probability density function of both convergence degrees and overlaps.

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

Article number | P06001 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2011 |

Issue number | 6 |

DOIs | |

Publication status | Published - Jun 2011 |

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### ASJC Scopus subject areas

- Statistics and Probability
- Statistical and Nonlinear Physics
- Statistics, Probability and Uncertainty

### Cite this

*Journal of Statistical Mechanics: Theory and Experiment*,

*2011*(6), [P06001]. https://doi.org/10.1088/1742-5468/2011/06/P06001

**Organization of signal flow in directed networks.** / Bányai, M.; Négyessy, L.; Bazsó, F.

Research output: Contribution to journal › Article

*Journal of Statistical Mechanics: Theory and Experiment*, vol. 2011, no. 6, P06001. https://doi.org/10.1088/1742-5468/2011/06/P06001

}

TY - JOUR

T1 - Organization of signal flow in directed networks

AU - Bányai, M.

AU - Négyessy, L.

AU - Bazsó, F.

PY - 2011/6

Y1 - 2011/6

N2 - Confining an answer to the question of whether and how the coherent operation of network elements is determined by the network structure is the topic of our work. We map the structure of signal flow in directed networks by analysing the degree of edge convergence and the overlap between the in-and output sets of an edge. Definitions of convergence degree and overlap are based on the shortest paths, thus they encapsulate global network properties. Using the defining notions of convergence degree and overlapping set we clarify the meaning of network causality and demonstrate the crucial role of chordless circles. In real-world networks the flow representation distinguishes nodes according to their signal transmitting, processing and control properties. The analysis of real-world networks in terms of flow representation was in accordance with the known functional properties of the network nodes. It is shown that nodes with different signal processing, transmitting and control properties are randomly connected at the global scale, while local connectivity patterns depart from randomness. The grouping of network nodes according to their signal flow properties was unrelated to the network's community structure. We present evidence that the signal flow properties of small-world-like, real-world networks cannot be reconstructed by algorithms used to generate small-world networks. Convergence degree values were calculated for regular oriented trees, and the probability density function for networks grown with the preferential attachment mechanism. For Erdos-Rényi graphs we calculated the probability density function of both convergence degrees and overlaps.

AB - Confining an answer to the question of whether and how the coherent operation of network elements is determined by the network structure is the topic of our work. We map the structure of signal flow in directed networks by analysing the degree of edge convergence and the overlap between the in-and output sets of an edge. Definitions of convergence degree and overlap are based on the shortest paths, thus they encapsulate global network properties. Using the defining notions of convergence degree and overlapping set we clarify the meaning of network causality and demonstrate the crucial role of chordless circles. In real-world networks the flow representation distinguishes nodes according to their signal transmitting, processing and control properties. The analysis of real-world networks in terms of flow representation was in accordance with the known functional properties of the network nodes. It is shown that nodes with different signal processing, transmitting and control properties are randomly connected at the global scale, while local connectivity patterns depart from randomness. The grouping of network nodes according to their signal flow properties was unrelated to the network's community structure. We present evidence that the signal flow properties of small-world-like, real-world networks cannot be reconstructed by algorithms used to generate small-world networks. Convergence degree values were calculated for regular oriented trees, and the probability density function for networks grown with the preferential attachment mechanism. For Erdos-Rényi graphs we calculated the probability density function of both convergence degrees and overlaps.

UR - http://www.scopus.com/inward/record.url?scp=79960241357&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79960241357&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/2011/06/P06001

DO - 10.1088/1742-5468/2011/06/P06001

M3 - Article

AN - SCOPUS:79960241357

VL - 2011

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

IS - 6

M1 - P06001

ER -