Laplacian spectral characterization of 3-rose graphs

Liu, Fenjin; Huang, Qiongxiang

doi:10.1016/j.laa.2013.07.029

Cited by 14 publications

(11 citation statements)

References 20 publications

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“…Since many real-life networks are scale-free, analytically unveiling the impact of heterogeneous topology on random walks is important for better understanding its dynamical behaviors and applications. In this section, we study analytically and numerically NBCRW, TURW and MERW on a class of heterogeneous rose graphs [65]. For a particular rose graph, we obtain closed-form expressions for stationary distribution and hitting times for these three random walks, and obtain numerical results for general rose graphs, which widely differ from one another.…”

Section: Analytical Results For Nbcbrw On Rose Graphsmentioning

confidence: 99%

Section: Analytical Results For Nbcbrw On Rose Graphsmentioning

confidence: 99%

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Non-Backtracking Centrality Based Random Walk on Networks

Lin

Zhang

2018

The Computer Journal

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Random walks are a fundamental tool for analyzing realistic complex networked systems and implementing randomized algorithms to solve diverse problems such as searching and sampling. For many real applications, their actual effect and convenience depend on the properties (e.g. stationary distribution and hitting time) of random walks, with biased random walks often outperforming traditional unbiased random walks (TURW). In this paper, we present a new class of biased random walks, non-backtracking centrality based random walks (NBCRW) on a network, where the walker prefers to jump to neighbors with high nonbacktracking centrality that has some advantages over eigenvector centrality. We study some properties of the non-backtracking matrix of a network, on the basis of which we propose a theoretical framework for fast computation of the transition probabilities, stationary distribution, and hitting times for NBCRW on the network. Within the paradigm, we study NBCRW on some model and real networks and compare the results with those corresponding to TURW and maximal entropy random walks (MERW), with the latter being biased random walks based on eigenvector centrality. We show that the behaviors of stationary distribution and hitting times for NBCRW widely differ from those associated with TURW and MERW, especially for heterogeneous networks.

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Section: Analytical Results For Nbcbrw On Rose Graphsmentioning

confidence: 99%

Section: Analytical Results For Nbcbrw On Rose Graphsmentioning

confidence: 99%

Non-Backtracking Centrality Based Random Walk on Networks

Lin

Zhang

2018

The Computer Journal

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“…Hence the corresponding coefficients are also equal. Thus, the following lemma follows from the Lemma 2.5 and Lemma 2.4: 26]). If G and H are two L-cospectral graphs, then…”

Section: Preliminariesmentioning

confidence: 90%

“…Note that the coalescence of two DLS graphs is not, necessarily DLS, see Figure 2. All paths, cycles, starlike trees, triangle free 2-graph are DLS [26,36,41,38]. In [24] it was shown that apart from two exceptional cases www.ejgta.org of order 6 and 7, all roses are DLS.…”

Section: Introductionmentioning

confidence: 99%

Tarantula graphs are determined by their Laplacian spectrum

Sharafdini

Abdian

2021

EJGTA

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A graph G is said to be determined by its Laplacian spectrum (DLS) if every graph with the same Laplacian spectrum is isomorphic to G. A graph which is a collection of hexagons (lengths of these cycles can be different) all sharing precisely one vertex is called a spinner graph. A tree with exactly one vertex of degree greater than 2 is called a starlike tree. If a spinner graph and a starlike tree are joined by merging their vertices of degree greater than 2, then the resulting graph is called a tarantula graph. It is known that spinner graphs and starlike trees are DLS. In this paper, we prove that tarantula graphs are determined by their Laplacian spectrum.

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“…Based on this equality, Liu and Huang [15] defined the following graph invariant for a graph G: 15]). If G and H are L-cospectral, then eðGÞ ¼ eðHÞ: Suppose Gða, b, c, dÞ is a graph with [18] proved that the graph Gða, b, c, dÞ is determined by its Laplacian spectrum.…”

Section: Theorem 23 ([6]mentioning

confidence: 99%

Laplacian spectral determination of path-friendship graphs

Oboudi

Abdian

Ашрафи

et al. 2021

AKCE International Journal of Graphs and Combinatorics

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A graph G is said to be determined by the spectrum of its Laplacian matrix (DLS) if every graph with the same spectrum is isomorphic to G. In some recent papers it is proved that the friendship graphs and starlike trees are DLS. If a friendship graph and a starlike tree are joined by merging their vertices of degree greater than two, then the resulting graph is called a path-friendship graph. In this paper, it is proved that the path-friendship graphs, a natural generalization of friendship graphs and starlike trees, are also DLS. Consequently, using these results we provide a solution for an open problem.

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Laplacian spectral characterization of 3-rose graphs

Cited by 14 publications

References 20 publications

Non-Backtracking Centrality Based Random Walk on Networks

Non-Backtracking Centrality Based Random Walk on Networks

Tarantula graphs are determined by their Laplacian spectrum

Laplacian spectral determination of path-friendship graphs

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