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Motifs in Graphs

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Encyclopedia of Complexity and Systems Science

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Definition of the Subject

Several nested levels of organization can be defined for any complex system, being many of such levels describable in terms of some type of networkpattern. In this context, complex networks both in nature and technology have been shown to display overabundance of some characteristic, small subgraphs(so called motifs) which appear to be characteristic of the class of network considered. These tiny modules offer a powerful way of classifyingnetworks and are the fingerprints of the rules generating network complexity.

Introduction

Complex systems c an be described, on a first approximation by means of a network [1,3,5,19]. In such a network, the typical components of the system (atoms, proteins, species, computers, humans or neurons)are simply nodes with no further structure. They are linked to others by means of an edge. The presence of such a link implies that there is some type ofcausal relation. Such relation can be the presence of a bond among atoms or...

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Abbreviations

Graph (network):

A set G of objects called points, nodes, or vertices connected by links called lines or edges.

Subgraph:

A subset of a graph G whose vertex and edge sets are subsets of those of G.

Modularity:

A network is called modular if it is subdivided into relatively autonomous, internally highly connected components.

Scale-free network:

A class of complex network showing a high heterogeneity in the distribution of links among its nodes. Such distribution decays as a power law.

Network motifs:

These are specific subgraphs that occur in different parts of a network at frequencies much higher than those found in randomized networks.

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Author information

Authors and Affiliations

  1. Complex Systems Lab, Parc de Recerca Biomedica de Barcelona, Barcelona, Spain

    Sergi Valverde

  2. Santa Fe Institute, Santa Fe, USA

    Ricard V. Solé

Authors
  1. Sergi Valverde
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  2. Ricard V. Solé
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Editor information

Editors and Affiliations

  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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© 2009 Springer-Verlag

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Valverde, S., Solé, R.V. (2009). Motifs in Graphs . In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_339

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