Mean Commute Time for Random Walks on Hierarchical Scale-Free Networks

Shang, Yilun

doi:10.1080/15427951.2012.685685

Cited by 18 publications

(8 citation statements)

References 35 publications

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“…Two-tree graphs have found many applications in complex networks see [6,13] and more information see e.g. [5,7,8,12]. In the past few decades, the topological indices due to their wide applications has been considered by many researchers.…”

Section: Introductionmentioning

confidence: 99%

Extremal trees for the Randić index

Jahanbani

Shooshtari

Shang

2022

Acta Universitatis Sapientiae, Mathematica

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Graph theory has applications in various fields due to offering important tools such as topological indices. Among the topological indices, the Randić index is simple and of great importance. The Randić index of a graph 𝒢 can be expressed as R ( G ) = ∑ x y ∈ Y ( G ) 1 τ ( x ) τ ( y ) R\left( G \right) = \sum\nolimits_{xy \in Y\left( G \right)} {{1 \over {\sqrt {\tau \left( x \right)\tau \left( y \right)} }}} , where 𝒴(𝒢) represents the edge set and τ(x) is the degree of vertex x. In this paper, considering the importance of the Randić index and applications two-trees graphs, we determine the first two minimums among the two-trees graphs.

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Section: Introductionmentioning

confidence: 99%

Extremal trees for the Randić index

Jahanbani

Shooshtari

Shang

2022

Acta Universitatis Sapientiae, Mathematica

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“…Considering longer paths, Local Path (LP) index [ 14 ] and Extended Resource Allocation (ERA) index [ 4 ] are proposed by adding the paths with length 3 to the CN index and RA index, respectively. Furthermore, many global indices are proposed by considering all the topological information between two endpoints, such as Katz index [ 15 ], SimRank [ 16 ], Average Commute Time (ACT, also called Mean Commute Time) [ 17 , 18 ] and Cosine Similarity Time (Cos+) [ 19 ]. In the real prediction, the global indices perform better than most of other methods, but they are not suitable for large-scale networks due to their high complexity.…”

Section: Introductionmentioning

confidence: 99%

A Potential Information Capacity Index for Link Prediction of Complex Networks Based on the Cannikin Law

Li¹,

Liu²,

Chen³

et al. 2019

Entropy

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Recently, a number of similarity-based methods have been proposed for link prediction of complex networks. Among these indices, the resource-allocation-based prediction methods perform very well considering the amount of resources in the information transmission process between nodes. However, they ignore the information channels and their information capacity in information transmission process between two endpoints. Motivated by the Cannikin Law, the definition of information capacity is proposed to quantify the information transmission capability between any two nodes. Then, based on the information capacity, a potential information capacity (PIC) index is proposed for link prediction. Empirical study on 15 datasets has shown that the PIC index we proposed can achieve a good performance, compared with eight mainstream baselines.

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“…Random constructions of Farey graph were explored in [ 16 , 17 ], where an edge is removed with some probability q and q ( t ) at each step, respectively. Also for a different purpose, Dorogovtsev et al [ 18 ] used a similar deterministic iteration process to generate pseudofractal scale-free networks (see also [ 19 ]). They have relevant but distinct properties with respect to our model.…”

Section: Introductionmentioning

confidence: 99%

Geometric Assortative Growth Model for Small-World Networks

Shang

2014

The Scientific World Journal

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It has been shown that both humanly constructed and natural networks are often characterized by small-world phenomenon and assortative mixing. In this paper, we propose a geometrically growing model for small-world networks. The model displays both tunable small-world phenomenon and tunable assortativity. We obtain analytical solutions of relevant topological properties such as order, size, degree distribution, degree correlation, clustering, transitivity, and diameter. It is also worth noting that the model can be viewed as a generalization for an iterative construction of Farey graphs.

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Mean Commute Time for Random Walks on Hierarchical Scale-Free Networks

Cited by 18 publications

References 35 publications

Extremal trees for the Randić index

Extremal trees for the Randić index

A Potential Information Capacity Index for Link Prediction of Complex Networks Based on the Cannikin Law

Geometric Assortative Growth Model for Small-World Networks

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