Resistance Distances and Kirchhoff Indices Under Graph Operations

Yang, Yujun; Yu, Yue

doi:10.1109/access.2020.2995935

Cited by 7 publications

(4 citation statements)

References 27 publications

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“…This expression shares similarities with the Kirchhoff index [33,[39][40][41] and other network indices [42].…”

Section: The Mathematical Description For Foncmentioning

confidence: 52%

On the Network Index of MAS with Layered Lattice-like Structures of Multiple Vertex-Related Parameters

Huang,

Yang,

et al. 2024

Symmetry

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In this article, a robust index named first-order network coherence (FONC) for the multi-agent systems (MASs) with layered lattice-like structure is studied via the angle of the graph spectra theory. The union operation of graphs is utilized to construct two pairs of non-isomorphic layered lattice-like structures, and the expression of the index is acquired by the approach of Laplacian spectra, then the corresponding asymptotic results are obtained. It is found that when the cardinality of the node sets of coronary substructures with better connectedness tends to infinity, the FONC of the whole network will have the same asymptotic behavior with the central lattice-like structure in the considered classic graph frameworks. The indices of the networks were simulated to illustrate the the asymptotic results, as described in the last section.

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“…This expression shares similarities with the Kirchhoff index [33,[39][40][41] and other network indices [42].…”

Section: The Mathematical Description For Foncmentioning

confidence: 52%

On the Network Index of MAS with Layered Lattice-like Structures of Multiple Vertex-Related Parameters

Huang,

Yang,

et al. 2024

Symmetry

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“…Algorithm 2 presents the calculation method of Kirchhoff index according to Eq. (15). Kf is closely related to the spectrum of the Laplacian matrix L G (for more details see [10]).…”

Section: Algorithm 1 Calculatermentioning

confidence: 99%

“…Note that r ij ≤ d ij , with equality if and only if there is only one path from i to j, where d ij represents the shortest path distance between i and j. Refer to [12]- [15] for different calculation methods of resistive distance. A main topic about resistance distance is its calculation in various graphs.…”

Section: Introductionmentioning

confidence: 99%

Novel Resistive Distance Descriptors on Complex Network

Zhou

Lin

et al. 2022

IEEE Access

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Large-scale complex network data poses significant challenges for the analytic ideas and tools to monitor and analyze complex networks. As classical structure descriptors, average path length (L), global and local network efficiency (E glob and E loc ), general and loop clustering coefficient (C 3 and D), play significant roles in complex network analysis. In this paper, we make use of resistive distance instead of the shortest path distance to suggest resistive distance descriptors, i.e., L r , Ω glob and Ω loc , Ω 3 and D r . We investigate all the resistive descriptors on classical WS, BA and ER models and find some interesting phenomenons. On one hand, L r and Ω 3 (resp., Ω glob and Ω loc ) can be used to characterize the features of small-word networks. On the other hand, L r , Ω 3 , and Ω glob can be utilized to measure network invulnerability. To access the effectiveness of the resistive distance descriptors, we conduct extensive numerical simulations on synthetic and real networks. In comparison with the baselines, the proposed metrics show competitive performance on classical network models and are more efficient for networks with small and medium size.

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“…Study of the Kirchhoff indices of various graphs is one of the fastest growing area of research in physics, chemistry, computer science, and mathematics. For some recent works in this context, the readers are refered to [18,19,21,7,10,13,15,12,11,17,16,1].…”

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confidence: 99%

Computing the Kirchhoff index and the Wiener index of spiro para-hexagonal cylinder chain

Reja,

2023

Preprint

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Kirchhoff index of a graph is given by the sum of inverses of non-zero Laplacian eigenvalues multiplied with the number of vertices of the graph. It has been studied for several linear and cylinder chains of chemically important graphs, so far. In this paper, we consider the spiro para-hexagonal cylinder chain and find its Kirchhoff index, Wiener index and number of spanning trees. We observe that like many other chain graphs, the ratio of Wiener index and Kirchhoff index approaches to 3 for large graphs belong to this class.

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Resistance Distances and Kirchhoff Indices Under Graph Operations

Cited by 7 publications

References 27 publications

On the Network Index of MAS with Layered Lattice-like Structures of Multiple Vertex-Related Parameters

On the Network Index of MAS with Layered Lattice-like Structures of Multiple Vertex-Related Parameters

Novel Resistive Distance Descriptors on Complex Network

Computing the Kirchhoff index and the Wiener index of spiro para-hexagonal cylinder chain

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