Network Science Meets Circuit Theory: Resistance Distance, Kirchhoff Index, and Foster’s Theorems With Generalizations and Unification

The emerging area of network science and engineering is concerned with the study of structural characteristics of networks, their impact on the dynamical behavior of systems as revealed through their topological properties, random evolution of networks, information spreading along a network, and so on. This area spans a wide range of applications in different disciplines. A topic of great interest in this area is the notion of network criticality. Most measures of network criticality are defined by the paths that flow through the nodes or edges. Since computing all the paths is computationally intractable, only the shortest paths are usually used for computing criticality metrics. Thus, measures that implicitly capture the impact of all the paths will be useful. The recently introduced concepts of the resistance distance and the Kirchhoff Index are two such measures. In this paper, we study these metrics and present several results that extend, generalize, and unify earlier works reported in the literature. In developing these results, the role of circuit theoretic concepts is emphasized. We also relate our works to Foster’s theorems and present a generalization that captures and retains the circuit theoretic elegance of Foster’s original theorems.

• Publication year

  2019

• Venue

  IEEE Transactions on Circuits and Systems Part 1: Regular Papers

• Publication date

  2019-03-01

• Fields of study

  Mathematics, Physics, Computer Science, Engineering

• Identifiers
  DOI 10.1109/TCSI.2018.2880601
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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