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Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients
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Two-point resistances in an Apollonian network.

Yingmin Shangguan1, Haiyan Chen1

  • 1School of Sciences, Jimei University, Xiamen Fujian 361021, People's Republic of China.

Physical Review. E
|January 20, 2018
PubMed
Summary

This study presents a recursive algorithm for calculating electrical resistance in Apollonian networks (A(k)). The method provides explicit resistance expressions for nodes within these complex resistor networks.

Area of Science:

  • Electrical Engineering
  • Graph Theory
  • Network Science

Background:

  • Calculating resistance in resistor networks is a fundamental problem in electrical and graph theory.
  • Apollonian networks (A(k)) are deterministic growing networks based on Apollonian packing.
  • Existing methods for resistance computation in complex networks can be computationally intensive.

Purpose of the Study:

  • To develop an efficient algorithm for computing the electrical resistance between any two nodes in Apollonian networks (A(k)).
  • To derive explicit mathematical expressions for resistances within A(k) networks using the developed algorithm.

Main Methods:

  • A novel recursive algorithm is designed for resistance computation.
  • The algorithm is applied to specific node pairs within the A(k) network structure.

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  • Symbolic computation and mathematical derivation are employed to obtain explicit formulas.

    • Main Results:

    • A recursive algorithm for calculating inter-node resistance in A(k) networks is successfully developed.
    • Explicit expressions for certain resistances within A(k) networks have been derived.
    • The algorithm demonstrates efficiency in handling the recursive structure of Apollonian networks.

    Conclusions:

    • The developed recursive algorithm provides an effective method for solving the resistance problem in A(k) networks.
    • The explicit expressions offer valuable insights into the electrical properties of Apollonian networks.
    • This work contributes to the understanding of complex network analysis and electrical theory.