scholarly journals Generating scale-free networks with adjustable clustering coefficient via random walks

2011 ◽  
Author(s):  
Carlos Herrera ◽  
Pedro J. Zufiria
Keyword(s):  
Random Walks ◽  
Clustering Coefficient ◽  
Scale Free ◽  
Scale Free Networks

scholarly journals Random walks in modular scale-free networks with multiple traps

2012 ◽  
Vol 85 (1) ◽  
Author(s):  
Zhongzhi Zhang ◽  
Yihang Yang ◽  
Yuan Lin
Keyword(s):  
Random Walks ◽  
Scale Free ◽  
Scale Free Networks

scholarly journals Scale-Free Networks with the Same Degree Distribution: Different Structural Properties

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
José H. H. Grisi-Filho ◽  
Raul Ossada ◽  
Fernando Ferreira ◽  
Marcos Amaku
Keyword(s):  
Structural Properties ◽  
Degree Distribution ◽  
Pearson Correlation ◽  
Clustering Coefficient ◽  
The Other ◽  
Scale Free ◽  
Component Size ◽  
Global Efficiency ◽  
Nearest Neighbours ◽  
Scale Free Networks

We have analysed some structural properties of scale-free networks with the same degree distribution. Departing from a degree distribution obtained from the Barabási-Albert (BA) algorithm, networks were generated using four additional different algorithms (Molloy-Reed, Kalisky, and two new models named A and B) besides the BA algorithm itself. For each network, we have calculated the following structural measures: average degree of the nearest neighbours, central point dominance, clustering coefficient, the Pearson correlation coefficient, and global efficiency. We found that different networks with the same degree distribution may have distinct structural properties. In particular, model B generates decentralized networks with a larger number of components, a smaller giant component size, and a low global efficiency when compared to the other algorithms, especially compared to the centralized BA networks that have all vertices in a single component, with a medium to high global efficiency. The other three models generate networks with intermediate characteristics between B and BA models. A consequence of this finding is that the dynamics of different phenomena on these networks may differ considerably.

scholarly journals Random walks and diameter of finite scale-free networks

2008 ◽  
Vol 387 (12) ◽  
pp. 3033-3038 ◽  
Author(s):  
Sungmin Lee ◽  
Soon-Hyung Yook ◽  
Yup Kim
Keyword(s):  
Random Walks ◽  
Scale Free ◽  
Scale Free Networks

scholarly journals Biased random walks in the scale-free networks with the disassortative degree correlation

2015 ◽  
Vol 64 (2) ◽  
pp. 028901
Author(s):  
Hu Yao-Guang ◽  
Wang Sheng-Jun ◽  
Jin Tao ◽  
Qu Shi-Xian
Keyword(s):  
Random Walks ◽  
Scale Free ◽  
Degree Correlation ◽  
Scale Free Networks ◽  
Biased Random Walks

Mean first passage time on a family of weighted directed hierarchical scale-free networks

2019 ◽  
Vol 33 (16) ◽  
pp. 1950179 ◽  
Author(s):  
Yu Gao ◽  
Zikai Wu
Keyword(s):  
Random Walks ◽  
Numerical Solutions ◽  
First Passage Time ◽  
Passage Time ◽  
Mean First Passage Time ◽  
First Passage ◽  
Scale Free ◽  
Weight Parameter ◽  
Scale Free Networks ◽  
Hierarchical Scale

Random walks on binary scale-free networks have been widely studied. However, many networks in real life are weighted and directed, the dynamic processes of which are less understood. In this paper, we firstly present a family of directed weighted hierarchical scale-free networks, which is obtained by introducing a weight parameter [Formula: see text] into the binary (1, 3)-flowers. Besides, each pair of nodes is linked by two edges with opposite direction. Secondly, we deduce the mean first passage time (MFPT) with a given target as a measure of trapping efficiency. The exact expression of the MFPT shows that both its prefactor and its leading behavior are dependent on the weight parameter [Formula: see text]. In more detail, the MFPT can grow sublinearly, linearly and superlinearly with varied [Formula: see text]. Last but not least, we introduce a delay parameter p to modify the transition probability governing random walk. Under this new scenario, we also derive the exact solution of the MFPT with the given target, the result of which illustrates that the delay parameter p can only change the coefficient of the MFPT and leave the leading behavior of MFPT unchanged. Both the analytical solutions of MFPT in two distinct scenarios mentioned above agree well with the corresponding numerical solutions. The analytical results imply that we can get desired transport efficiency by tuning weight parameter [Formula: see text] and delay parameter p. This work may help to advance the understanding of random walks in general directed weighted scale-free networks.

scholarly journals Detecting differences in the topology of scale-free networks grown under time-dynamic topological fitness

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Dimitrios Tsiotas
Keyword(s):  
Preferential Attachment ◽  
Clustering Coefficient ◽  
The Other ◽  
Eigenvector Centrality ◽  
Hybrid Fitness ◽  
Time Dynamic ◽  
Scale Free ◽  
Time Dynamics ◽  
Scale Free Networks ◽  
Fitness Distribution

Abstract The fitness model was introduced in the literature to expand the Barabasi-Albert model’s generative mechanism, which produces scale-free networks under the control of degree. However, the fitness model has not yet been studied in a comprehensive context because most models are built on invariant fitness as the network grows and time-dynamics mainly concern new nodes joining the network. This mainly static consideration restricts fitness in generating scale-free networks only when the underlying fitness distribution is power-law, a fact which makes the hybrid fitness models based on degree-driven preferential attachment to remain the most attractive models in the literature. This paper advances the time-dynamic conceptualization of fitness, by studying scale-free networks generated under topological fitness that changes as the network grows, where the fitness is controlled by degree, clustering coefficient, betweenness, closeness, and eigenvector centrality. The analysis shows that growth under time-dynamic topological fitness is indifferent to the underlying fitness distribution and that different topological fitness generates networks of different topological attributes, ranging from a mesh-like to a superstar-like pattern. The results also show that networks grown under the control of betweenness centrality outperform the other networks in scale-freeness and the majority of the other topological attributes. Overall, this paper contributes to broadening the conceptualization of fitness to a more time-dynamic context.

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