scholarly journals Using Spectral Radius Ratio for Node Degree to Analyze the Evolution of Complex Networks

2015 ◽  
Vol 7 (3) ◽  
pp. 1-12 ◽  
Author(s):  
Natarajan Meghanathan
Keyword(s):  
Complex Networks ◽  
Spectral Radius ◽  
Radius Ratio ◽  
Node Degree

Efficient weighting strategy for enhancing synchronizability of complex networks

2018 ◽  
Vol 32 (11) ◽  
pp. 1850128 ◽  
Author(s):  
Youquan Wang ◽  
Feng Yu ◽  
Shucheng Huang ◽  
Juanjuan Tu ◽  
Yan Chen
Keyword(s):  
Complex Networks ◽  
Structural Properties ◽  
Real World ◽  
Centrality Measures ◽  
Node Degree ◽  
Scale Free ◽  
High Propensity ◽  
Network Link ◽  
Weighting Strategy ◽  
Weighting Methods

Networks with high propensity to synchronization are desired in many applications ranging from biology to engineering. In general, there are two ways to enhance the synchronizability of a network: link rewiring and/or link weighting. In this paper, we propose a new link weighting strategy based on the concept of the neighborhood subgroup. The neighborhood subgroup of a node i through node j in a network, i.e. [Formula: see text], means that node u belongs to [Formula: see text] if node u belongs to the first-order neighbors of j (not include i). Our proposed weighting schema used the local and global structural properties of the networks such as the node degree, betweenness centrality and closeness centrality measures. We applied the method on scale-free and Watts–Strogatz networks of different structural properties and show the good performance of the proposed weighting scheme. Furthermore, as model networks cannot capture all essential features of real-world complex networks, we considered a number of undirected and unweighted real-world networks. To the best of our knowledge, the proposed weighting strategy outperformed the previously published weighting methods by enhancing the synchronizability of these real-world networks.

scholarly journals SZNAJD MODEL WITH SYNCHRONOUS UPDATING ON COMPLEX NETWORKS

2005 ◽  
Vol 16 (07) ◽  
pp. 1149-1161 ◽  
Author(s):  
YU-SONG TU ◽  
A. O. SOUSA ◽  
LING-JIANG KONG ◽  
MU-REN LIU
Keyword(s):  
Complex Networks ◽  
Small World ◽  
System Size ◽  
The State ◽  
Clustering Coefficient ◽  
Square Lattice ◽  
Node Degree ◽  
Scale Free ◽  
Free Network ◽  
Formation Step

We analyze the evolution of Sznajd Model with synchronous updating in several complex networks. Similar to the model on square lattice, we have found a transition between the state with nonconsensus and the state with complete consensus in several complex networks. Furthermore, by adjusting the network parameters, we find that a large clustering coefficient does not favor development of a consensus. In particular, in the limit of large system size with the initial concentration p =0.5 of opinion +1, a consensus seems to be never reached for the Watts–Strogatz small-world network, when we fix the connectivity k and the rewiring probability ps; nor for the scale-free network, when we fix the minimum node degree m and the triad formation step probability pt.

THE APPLICATION OF SEMIDEFINITE INTEGER PROGRAMMING MODEL FOR THE SIMULATION OF COMPLEX NETWORKS

2015 ◽  
Vol 18 (03n04) ◽  
pp. 1550015
Author(s):  
JIAO BO ◽  
LU ZHI-YONG ◽  
SHI JIAN-MAI
Keyword(s):  
Integer Programming ◽  
Complex Networks ◽  
Branch And Bound ◽  
Structural Design ◽  
Spectral Distribution ◽  
Programming Model ◽  
Node Degree ◽  
Integer Programming Model ◽  
Spectral Distributions ◽  
Feasible Solutions

Semidefinite integer programming model is an accurate tool for the structural design of networks. In this paper, we propose a semidefinite integer programming model with the constraints of spectral distributions and node degree distributions for the simulation of complex networks. Also, the feasible solutions and branch-and-bound solving algorithms of the model are designed. Based on eight metrics (e.g., spectral distribution, node degree distribution, clustering coefficients, etc.), the validity and practicability of the proposed method are illustrated.

Link prediction based on nonequilibrium cooperation effect

2018 ◽  
Vol 32 (11) ◽  
pp. 1850128 ◽  
Author(s):  
LanXi Li ◽  
XuZhen Zhu ◽  
Hui Tian
Keyword(s):  
Numerical Analysis ◽  
Theoretical Analysis ◽  
Complex Networks ◽  
Real World ◽  
Link Prediction ◽  
Prediction Method ◽  
Large Degree ◽  
Node Degree ◽  
Improve Accuracy

Link prediction in complex networks has become a common focus of many researchers. But most existing methods concentrate on neighbors, and rarely consider degree heterogeneity of two endpoints. Node degree represents the importance or status of endpoints. We describe the large-degree heterogeneity as the nonequilibrium between nodes. This nonequilibrium facilitates a stable cooperation between endpoints, so that two endpoints with large-degree heterogeneity tend to connect stably. We name such a phenomenon as the nonequilibrium cooperation effect. Therefore, this paper proposes a link prediction method based on the nonequilibrium cooperation effect to improve accuracy. Theoretical analysis will be processed in advance, and at the end, experiments will be performed in 12 real-world networks to compare the mainstream methods with our indices in the network through numerical analysis.

scholarly journals Critical Nodes Identification in Complex Networks

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 123 ◽  
Author(s):  
Haihua Yang ◽  
Shi An
Keyword(s):  
Complex Networks ◽  
Information Exchange ◽  
Network Connectivity ◽  
Node Degree ◽  
Structural Holes ◽  
Structural Hole ◽  
Node Importance ◽  
Critical Nodes ◽  
Unweighted Network ◽  
Collective Influence

Critical nodes identification in complex networks is significance for studying the survivability and robustness of networks. The previous studies on structural hole theory uncovered that structural holes are gaps between a group of indirectly connected nodes and intermediaries that fill the holes and serve as brokers for information exchange. In this paper, we leverage the property of structural hole to design a heuristic algorithm based on local information of the network topology to identify node importance in undirected and unweighted network, whose adjacency matrix is symmetric. In the algorithm, a node with a larger degree and greater number of structural holes associated with it, achieves a higher importance ranking. Six real networks are used as test data. The experimental results show that the proposed method not only has low computational complexity, but also outperforms degree centrality, k-shell method, mapping entropy centrality, the collective influence algorithm, DDN algorithm that based on node degree and their neighbors, and random ranking method in identifying node importance for network connectivity in complex networks.

scholarly journals STRENGTH DISTRIBUTION IN DERIVATIVE NETWORKS

2005 ◽  
Vol 16 (07) ◽  
pp. 1097-1105 ◽  
Author(s):  
LUCIANO DA FONTOURA COSTA ◽  
GONZALO TRAVIESO
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Lower Limit ◽  
Network Model ◽  
Power Law ◽  
Neuronal Networks ◽  
Strength Distribution ◽  
Node Degree ◽  
Upper Limit ◽  
The Difference

This article describes a complex network model whose weights are proportional to the difference between uniformly distributed "fitness" values assigned to the nodes. It is shown both analytically and experimentally that the strength density (i.e., the weighted node degree) for this model, called derivative complex networks, follows a power law with exponent γ<1 if the fitness has an upper limit and γ>1 if the fitness has no upper limit but a positive lower limit. Possible implications for neuronal networks topology and dynamics are also discussed.

scholarly journals Random complex networks

2014 ◽  
Vol 1 (3) ◽  
pp. 357-367 ◽  
Author(s):  
Michael Small ◽  
Lvlin Hou ◽  
Linjun Zhang
Keyword(s):  
Complex Networks ◽  
Degree Distribution ◽  
Preferential Attachment ◽  
Small World ◽  
Node Degree ◽  
Scale Free ◽  
Wide Range ◽  
Random Complex ◽  
Law Degree ◽  
Attachment Process

Abstract Exactly what is meant by a ‘complex’ network is not clear; however, what is clear is that it is something other than a random graph. Complex networks arise in a wide range of real social, technological and physical systems. In all cases, the most basic categorization of these graphs is their node degree distribution. Particular groups of complex networks may exhibit additional interesting features, including the so-called small-world effect or being scale-free. There are many algorithms with which one may generate networks with particular degree distributions (perhaps the most famous of which is preferential attachment). In this paper, we address what it means to randomly choose a network from the class of networks with a particular degree distribution, and in doing so we show that the networks one gets from the preferential attachment process are actually highly pathological. Certain properties (including robustness and fragility) which have been attributed to the (scale-free) degree distribution are actually more intimately related to the preferential attachment growth mechanism. We focus here on scale-free networks with power-law degree sequences—but our methods and results are perfectly generic.

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