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The Topology of Technology Graphs: Small World Patterns in Electronic Circuits

Author

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  • Ramon Ferrer i Cancho
  • Christiaan Janssen
  • Ricard V. Solé

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 analyse 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 SW behavior. We conjecture that the SW 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 , 11149 (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.

Suggested Citation

  • Ramon Ferrer i Cancho & Christiaan Janssen & Ricard V. Solé, 2001. "The Topology of Technology Graphs: Small World Patterns in Electronic Circuits," Working Papers 01-05-029, Santa Fe Institute.
    • Handle: RePEc:wop:safiwp:01-05-029
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    Cited by:

    1. Comellas, Francesc & Miralles, Alícia & Liu, Hongxiao & Zhang, Zhongzhi, 2013. "The number of spanning trees of an infinite family of outerplanar, small-world and self-similar graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(12), pages 2803-2806.
    2. Cárdenas, J.P. & Mouronte, M.L. & Benito, R.M. & Losada, J.C., 2010. "Compatibility as underlying mechanism behind the evolution of networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(8), pages 1789-1798.
    3. Dan Braha & Yaneer Bar-Yam, 2007. "The Statistical Mechanics of Complex Product Development: Empirical and Analytical Results," Management Science, INFORMS, vol. 53(7), pages 1127-1145, July.
    4. Raúl M. Falcón & Nagaraj Mohanapriya & Venkitachalam Aparna, 2022. "Optimal Shadow Allocations of Secret Sharing Schemes Arisen from the Dynamic Coloring of Extended Neighborhood Coronas," Mathematics, MDPI, vol. 10(12), pages 1-14, June.
    5. Shang, Yilun, 2021. "Generalized k-cores of networks under attack with limited knowledge," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    6. Pablo Medina & Natalia Ariza & Pablo Navas & Fernando Rojas & Gina Parody & Juan Alejandro Valdivia & Roberto Zarama & Juan Felipe Penagos, 2018. "An Unintended Effect of Financing the University Education of the Most Brilliant and Poorest Colombian Students: The Case of the Intervention of the Ser Pilo Paga Program," Complexity, Hindawi, vol. 2018, pages 1-9, December.
    7. Selen Onel & Abe Zeid & Sagar Kamarthi, 2011. "The structure and analysis of nanotechnology co-author and citation networks," Scientometrics, Springer;Akadémiai Kiadó, vol. 89(1), pages 119-138, October.
    8. Huang, Chung-Yuan & Chin, Wei-Chien-Benny & Fu, Yu-Hsiang & Tsai, Yu-Shiuan, 2019. "Beyond bond links in complex networks:Local bridges, global bridges and silk links," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    9. Lucas Cuadra & Sancho Salcedo-Sanz & Javier Del Ser & Silvia Jiménez-Fernández & Zong Woo Geem, 2015. "A Critical Review of Robustness in Power Grids Using Complex Networks Concepts," Energies, MDPI, vol. 8(9), pages 1-55, August.
    10. Miralles, Alicia & Comellas, Francesc & Chen, Lichao & Zhang, Zhongzhi, 2010. "Planar unclustered scale-free graphs as models for technological and biological networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(9), pages 1955-1964.
    11. Coninck, José C.P. & Ferrari, Fabiano A.S. & Reis, Adriane S. & Iarosz, Kelly C. & Caldas, Iberê L. & Batista, Antonio M. & Viana, Ricardo L., 2020. "Network properties of healthy and Alzheimer brains," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    12. Cárdenas, J.P. & Mouronte, M.L. & Moyano, L.G. & Vargas, M.L. & Benito, R.M., 2010. "On the robustness of Spanish telecommunication networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(19), pages 4209-4216.
    13. Comellas, Francesc & Miralles, Alicia, 2009. "Modeling complex networks with self-similar outerplanar unclustered graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(11), pages 2227-2233.
    14. Laurienti, Paul J. & Joyce, Karen E. & Telesford, Qawi K. & Burdette, Jonathan H. & Hayasaka, Satoru, 2011. "Universal fractal scaling of self-organized networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3608-3613.
    15. Jin, Yi & Zhang, Qingyuan & Chen, Yunxia & Lu, Zhendan & Zu, Tianpei, 2023. "Cascading failures modeling of electronic circuits with degradation using impedance network," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    16. Nie, Tingyuan & Fan, Bo & Wang, Zhenhao, 2022. "Complexity and robustness of weighted circuit network of placement," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 598(C).

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    Keywords

    Small world; electronic devices; networks; graph theory; evolvable hardware; statistical physics;
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