Topology of technology graphs: Small world patterns in electronic circuits

Ramon Ferrer i Cancho, Christiaan Janssen, and Ricard V. Solé
Phys. Rev. E 64, 046119 – Published 24 September 2001
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Abstract

Recent theoretical studies and extensive data analyses have revealed a common feature displayed by biological, social, and technological networks: the presence of small world patterns. Here we analyze this problem by using several graphs obtained from one of the most common technological systems: electronic circuits. It is shown that both analogic and digital circuits exhibit small world behavior. We conjecture that the small world pattern arises from the compact design in which many elements share a small, close physical neighborhood plus the fact that the system must define a single connected component (which requires shortcuts connecting different integrated clusters). The degree distributions displayed are consistent with a conjecture concerning the sharp cutoffs associated to the presence of costly connections [Amaral et al., Proc. Natl. Acad. Sci. USA 97, 11 149 (2000)], thus providing a limit case for the classes of universality of small world patterns from real, artificial networks. The consequences for circuit design are outlined.

  • Received 22 May 2001

DOI:https://doi.org/10.1103/PhysRevE.64.046119

©2001 American Physical Society

Authors & Affiliations

Ramon Ferrer i Cancho1, Christiaan Janssen1, and Ricard V. Solé1,2,3,*

  • 1Complex Systems Research Group, FEN-UPC, Campus Nord, B4-B5, Barcelona 08034, Spain
  • 2Santa Fe Institute, 1399 Hyde Park Road, New Mexico 87501
  • 3NASA–Associated Astrobiology Institute, CSIC/INTA, Carretera del Ajalvir km 4, Madrid, Spain

  • *Email address: ricard@ants.upc.es, sole@santafe.edu

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Vol. 64, Iss. 4 — October 2001

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