scholarly journals COMPARISON OF ISING MAGNET ON DIRECTED VERSUS UNDIRECTED ERDÖS–RÉNYI AND SCALE-FREE NETWORKS

2007 ◽  
Vol 18 (01) ◽  
pp. 53-60 ◽  
Author(s):  
M. A. SUMOUR ◽  
A. H. EL-ASTAL ◽  
F. W. S. LIMA ◽  
M. M. SHABAT ◽  
H. M. KHALIL
Keyword(s):  
Spontaneous Magnetization ◽  
The Other ◽  
Directed Network ◽  
Equilibration Time ◽  
Arrhenius Law ◽  
Power Law Distribution ◽  
Scale Free ◽  
Scale Free Networks ◽  
Low Probability ◽  
Ising Magnet

Scale-free networks are a recently developed approach to model the interactions found in complex natural and man-made systems. Such networks exhibit a power-law distribution of node link (degree) frequencies n(k) in which a small number of highly connected nodes predominate over a much greater number of sparsely connected ones. In contrast, in an Erdös–Renyi network each of N sites is connected to every site with a low probability p (of the order of 1/N). Then the number k of neighbors will fluctuate according to a Poisson distribution. One can instead assume that each site selects exactly k neighbors among the other sites. Here we compare in both cases the usual network with the directed network, when site A selects site B as a neighbor, and then B influences A but A does not influence B. As we change from undirected to directed scale-free networks, the spontaneous magnetization vanishes after an equilibration time following an Arrhenius law, while the directed ER networks have a positive Curie temperature.

Scale-Free Networks Based on the Value of Interest

2013 ◽  
Vol 753-755 ◽  
pp. 2959-2962
Author(s):  
Jun Tao Yang ◽  
Hui Wen Deng
Keyword(s):  
Network Model ◽  
Power Law ◽  
Scale Free Network ◽  
Power Law Distribution ◽  
Scale Free ◽  
Distribution Property ◽  
Scale Free Networks ◽  
Free Model ◽  
Free Network ◽  
Interest Model

Assigning the value of interest to each node in the network, we give a scale-free network model. The value of interest is related to the fitness and the degree of the node. Experimental results show that the interest model not only has the characteristics of the BA scale-free model but also has the characteristics of fitness model, and the network has a power-law distribution property.

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 Controllability and Optimization of Complex Networks Based on Bridges

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Lifu Wang ◽  
Guotao Zhao ◽  
Zhi Kong ◽  
Yunkang Zhao
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Betweenness Centrality ◽  
The Other ◽  
Connected Components ◽  
Scale Free ◽  
Scale Free Networks ◽  
Model Networks ◽  
Simulation Results ◽  
And Control

In a complex network, each edge has different functions on controllability of the whole network. A network may be out of control due to failure or attack of some specific edges. Bridges are a kind of key edges whose removal will disconnect a network and increase connected components. Here, we investigate the effects of removing bridges on controllability of network. Various strategies, including random deletion of edges, deletion based on betweenness centrality, and deletion based on degree of source or target nodes, are used to compare with the effect of removing bridges. It is found that the removing bridges strategy is more efficient on reducing controllability than the other strategies of removing edges for ER networks and scale-free networks. In addition, we also found the controllability robustness under edge attack is related to the average degree of complex networks. Therefore, we propose two optimization strategies based on bridges to improve the controllability robustness of complex networks against attacks. The effectiveness of the proposed strategies is demonstrated by simulation results of some model networks. These results are helpful for people to understand and control spreading processes of epidemic across different paths.

Temporal Variation of the Node Centrality Metrics for Scale-Free Networks

2018 ◽  
pp. 78-97
Keyword(s):  
Temporal Variation ◽  
Closeness Centrality ◽  
The Other ◽  
Centrality Measures ◽  
Degree Centrality ◽  
Eigenvector Centrality ◽  
Scale Free ◽  
Centrality Metrics ◽  
Scale Free Networks ◽  
Free Network

Scale-free networks are a type of complex networks in which the degree distribution of the nodes is according to the power law. In this chapter, the author uses the widely studied Barabasi-Albert (BA) model to simulate the evolution of scale-free networks and study the temporal variation of degree centrality, eigenvector centrality, closeness centrality, and betweenness centrality of the nodes during the evolution of a scale-free network according to the BA model. The model works by adding new nodes to the network, one at a time, with the new node connected to m of the currently existing nodes. Accordingly, nodes that have been in the network for a longer time have greater chances of acquiring more links and hence a larger degree centrality. While the degree centrality of the nodes has been observed to show a concave down pattern of increase with time, the temporal (time) variation of the other centrality measures has not been analyzed until now.

scholarly journals On dynamic network security: A random decentering algorithm on graphs

2018 ◽  
Vol 16 (1) ◽  
pp. 656-668 ◽  
Author(s):  
M.T. Trobajo ◽  
J. Cifuentes-Rodríguez ◽  
M.V. Carriegos
Keyword(s):  
Network Security ◽  
Dynamic Network ◽  
Closeness Centrality ◽  
The Other ◽  
Minimal Cost ◽  
Basic Principles ◽  
Scale Free ◽  
Scale Free Networks ◽  
The Given ◽  
Unweighted Graph

AbstractRandom Decentering Algorithm (RDA) on a undirected unweighted graph is defined and tested over several concrete scale-free networks. RDA introduces ancillary nodes to the given network following basic principles of minimal cost, density preservation, centrality reduction and randomness. First simulations over scale-free networks show that RDA gives a significant decreasing of both betweenness centrality and closeness centrality and hence topological protection of network is improved. On the other hand, the procedure is performed without significant change of the density of connections of the given network. Thus ancillae are not distinguible from real nodes (in a straightforward way) and hence network is obfuscated to potential adversaries by our manipulation.

Edge Weight Method for Community Detection on Mixed Scale-Free Networks

2015 ◽  
Vol 24 (02) ◽  
pp. 1540007 ◽  
Author(s):  
Sorn Jarukasemratana ◽  
Tsuyoshi Murata
Keyword(s):  
Normal Distribution ◽  
Community Detection ◽  
Power Law ◽  
The Other ◽  
Detection Methods ◽  
Node Degree ◽  
Edge Weight ◽  
Scale Free ◽  
Scale Free Networks ◽  
Weight Method

In this paper, we proposed an edge weight method for performing a community detection on mixed scale-free networks.We use the phrase “mixed scale-free networks” for networks where some communities have node degree that follows a power law similar to scale-free networks, while some have node degree that follows normal distribution. In this type of network, community detection algorithms that are designed for scale-free networks will have reduced accuracy because some communities do not have scale-free properties. On the other hand, algorithms that are not designed for scale-free networks will also have reduced accuracy because some communities have scale-free properties. To solve this problem, our algorithm consists of two community detection steps; one is aimed at extracting communities whose node degree follows power law distribution (scale-free), while the other one is aimed at extracting communities whose node degree follows normal distribution (non scale-free). To evaluate our method, we use NMI — Normalized Mutual Information — to measure our results on both synthetic and real-world datasets comparing with both scale-free and non scale-free community detection methods. The results show that our method outperforms all other based line methods on mixed 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.

EXACT SOLUTIONS FOR AVERAGE TRAPPING TIME OF RANDOM WALKS ON WEIGHTED SCALE-FREE NETWORKS

Fractals ◽  
2017 ◽  
Vol 25 (02) ◽  
pp. 1750013 ◽  
Author(s):  
CHANGMING XING ◽  
YIGONG ZHANG ◽  
JUN MA ◽  
LIN YANG ◽  
LEI GUO
Keyword(s):  
Random Walks ◽  
Exact Solutions ◽  
Weight Distribution ◽  
Close Relation ◽  
The Other ◽  
Trapping Time ◽  
Scale Free ◽  
Weight Parameter ◽  
Scale Free Networks ◽  
Fractal Network

In this paper, we present two deterministic weighted scale-free networks controlled by a weight parameter [Formula: see text]. One is fractal network, the other one is non-fractal network, while they have the same weight distribution when the parameter [Formula: see text] is identical. Based on their special network structure, we study random walks on network with a trap located at a fixed node. For each network, we calculate exact solutions for average trapping time (ATT). Analyzing and comparing the obtained solutions, we find that their ATT all grow asymptotically as a power-law function of network order (number of nodes) with the exponent [Formula: see text] dependent on the weight parameter, but their exponent [Formula: see text] are obviously different, one is an increasing function of [Formula: see text], while the other is opposite. Collectively, all the obtained results show that the efficiency of trapping on weighted Scale-free networks has close relation to the weight distribution, but there is no stable positive or negative correlation between the weight distribution and the trapping time on different networks. We hope these results given in this paper could help us get deeper understanding about the weight distribution on the property and dynamics of scale-free networks.

MODELING OF CYCLIC TOPOLOGY IN SCALE-FREE NETWORKS

2006 ◽  
Vol 20 (23) ◽  
pp. 1489-1496
Author(s):  
HYUN-JOO KIM ◽  
YEON-MU CHOI
Keyword(s):  
Network Model ◽  
Preferential Attachment ◽  
The Other ◽  
The Real ◽  
Scale Free ◽  
Scale Free Networks ◽  
Growing Network ◽  
Attachment Process

We introduce a growing network model describing the cyclic topology of scale-free networks. In the model, we add new vertices and attach new edges between already existing vertices. The new edges are added by two different processes which is controlled by a parameter p. One is the neighbor attachment process which makes the network become cyclic, and the other is the preferential attachment process which results in the scale-free property of the network. We measure the cyclic coefficient R for various p and find that it linearly depend on p. Also by measuring the distribution of the local cyclic coefficient we survey the change of cyclic topology in the networks for varing p and compare it to the real networks.

Second-order centrality correlation in scale-free networks

2015 ◽  
Vol 26 (10) ◽  
pp. 1550116 ◽  
Author(s):  
Meilei Lv ◽  
Xinling Guo ◽  
Jiaquan Chen ◽  
Zhe-Ming Lu ◽  
Tingyuan Nie
Keyword(s):  
Second Order ◽  
Degree Centrality ◽  
Apparent Difference ◽  
Power Law Distribution ◽  
Scale Free ◽  
Degree Correlation ◽  
Critical Nodes ◽  
Scale Free Networks ◽  
Node Removal ◽  
Assortative Network

Scale-free networks in which the degree displays a power-law distribution can be classified into assortative, disassortative, and neutral networks according to their degree–degree correlation. The second-order centrality proposed in a distributed computation manner is quick-calculated and accurate to identify critical nodes. We explore the second-order centrality correlation (SOC) for each type of the scale-free networks. The SOC–SOC correlation in assortative network and neutral network behaves similarly to the degree–degree correlation, while it behaves an apparent difference in disassortative networks. Experiments show that the invulnerability of most of scale-free networks behaves similarly under the node removal ordering by SOC centrality and degree centrality, respectively. The netscience network and the Yeast network behave a little differently because they are native disconnecting networks.

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