Organization of signal flow in directed networks

M. Bányai, L. Négyessy, F. Bazsó

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish
Article numberP06001
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2011
Issue number6
DOIs
Publication statusPublished - Jun 2011

Fingerprint

Directed Network
Overlap
Signal Control
Vertex of a graph
Network Structure
Probability density function
Signal Processing
Local Connectivity
probability density functions
Preferential Attachment
signal processing
Small-world Network
Community Structure
Small World
Causality
Erdös
Shortest path
Grouping
Randomness
Overlapping

ASJC Scopus subject areas

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

Cite this

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

In: Journal of Statistical Mechanics: Theory and Experiment, Vol. 2011, No. 6, P06001, 06.2011.

Research output: Contribution to journalArticle

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