SNAM

2016 ◽  
pp. 215-236 ◽  
Author(s):  
Bassant Youssef ◽  
Scott F. Midkiff ◽  
Mohamed R. M. Rizk
Keyword(s):  
Community Structure ◽  
Complex Networks ◽  
Degree Distribution ◽  
Network Models ◽  
Small World ◽  
Clustering Coefficient ◽  
Network Nodes ◽  
Scale Free ◽  
Complex Network Models ◽  
Novel Model

Complex networks are characterized by having a scale-free power-law (PL) degree distribution, a small world phenomenon, a high average clustering coefficient, and the emergence of community structure. Most proposed models did not incorporate all of these statistical properties and neglected incorporating the heterogeneous nature of network nodes. Even proposed heterogeneous complex network models were not generalized for different complex networks. We define a novel aspect of node-heterogeneity which is the node connection standard heterogeneity. We introduce our novel model “settling node adaptive model” SNAM which reflects this new nodes' heterogeneous aspect. SNAM was successful in preserving PL degree distribution, small world phenomenon and high clustering coefficient of complex networks. A modified version of SNAM shows the emergence of community structure. We prove using mathematical analysis that networks generated using SNAM have a PL degree distribution.

scholarly journals Studies on the Decrease Mechanisms of Typical Complex Networks

2021 ◽  
Author(s):  
Yuhu Qiu ◽  
Tianyang Lyu ◽  
Xizhe Zhang ◽  
Ruozhou Wang
Keyword(s):  
Average Length ◽  
Shortest Paths ◽  
Real Life ◽  
Network Models ◽  
Small World ◽  
Clustering Coefficient ◽  
Network Growth ◽  
Scale Free ◽  
Complex Network Models ◽  
High Degree

Network decrease caused by the removal of nodes is an important evolution process that is paralleled with network growth. However, many complex network models usually lacked a sound decrease mechanism. Thus, they failed to capture how to cope with decreases in real life. The paper proposed decrease mechanisms for three typical types of networks, including the ER networks, the WS small-world networks and the BA scale-free networks. The proposed mechanisms maintained their key features in continuous and independent decrease processes, such as the random connections of ER networks, the long-range connections based on nearest-coupled network of WS networks and the tendency connections and the scale-free feature of BA networks. Experimental results showed that these mechanisms also maintained other topology characteristics including the degree distribution, clustering coefficient, average length of shortest-paths and diameter during decreases. Our studies also showed that it was quite difficult to find an efficient decrease mechanism for BA networks to withstand the continuous attacks at the high-degree nodes, because of the unequal status of nodes.

Social Community Classification Based on Laplacian Spectrum Feature

2011 ◽  
Vol 63-64 ◽  
pp. 142-146
Author(s):  
Bo Wang ◽  
Yi Qiong Xu ◽  
Yao Ming Zhou
Keyword(s):  
Community Structure ◽  
Common Property ◽  
Distance Measure ◽  
Network Models ◽  
Small World ◽  
Laplacian Spectrum ◽  
Free Graph ◽  
Scale Free ◽  
Spectrum Feature ◽  
Complex Network Models

Community structure is a common property that exists in social networks. Community structure analysis is important for understanding network structure and analyzing the network characteristics. Recently community detecting methods are reported continually, but within community the structure is still complex. This paper proposed a method applied to classify community by using Laplacian spectrum feature, and defined the distance measure between the features extracted from difference community. As experiments, this paper studied three complex network models: the random graph of Erdös-Rényi, the small world of Watts and Strogatz and the scale-free graph, and classified them based on Laplacian spectrum feature successfully. The result shows the Laplacian spectrum feature and similarity measure are effective for classification.

scholarly journals On the Distributions of Subgraph Centralities in Complex Networks

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Faxu Li ◽  
Liang Wei ◽  
Haixing Zhao ◽  
Feng Hu
Keyword(s):  
Complex Networks ◽  
Probability Distributions ◽  
Network Connectivity ◽  
Network Models ◽  
Small World ◽  
Small World Networks ◽  
Power Law Distribution ◽  
Scale Free ◽  
Scale Free Networks ◽  
Complex Network Models

Subgraph centrality measure characterizes the participation of each node in all subgraphs in a network. Smaller subgraphs are given more weight than large ones, which makes this measure appropriate for characterizing network motifs. This measure is better in being able to discriminate the nodes of a network than alternate measures. In this paper, the important issue of subgraph centrality distributions is investigated through theory-guided extensive numerical simulations, for three typical complex network models, namely, the ER random-graph networks, WS small-world networks, and BA scale-free networks. It is found that these three very different types of complex networks share some common features, particularly that the subgraph centrality distributions in increasing order are all insensitive to the network connectivity characteristics, and also found that the probability distributions of subgraph centrality of the ER and of the WS models both follow the gamma distribution, and the BA scale-free networks exhibit a power-law distribution with an exponential cutoff.

SCALE-FREE AND SMALL-WORLD PROPERTIES OF A SPECIAL HIERARCHICAL NETWORK

Fractals ◽  
2019 ◽  
Vol 27 (02) ◽  
pp. 1950010
Author(s):  
DAOHUA WANG ◽  
YUMEI XUE ◽  
QIAN ZHANG ◽  
MIN NIU
Keyword(s):  
Degree Distribution ◽  
Path Length ◽  
Small World ◽  
Average Path Length ◽  
Clustering Coefficient ◽  
Hierarchical Network ◽  
Scale Free

Many real systems behave similarly with scale-free and small-world structures. In this paper, we generate a special hierarchical network and based on the particular construction of the graph, we aim to present a study on some properties, such as the clustering coefficient, average path length and degree distribution of it, which shows the scale-free and small-world effects of this network.

COMPLEX NETWORKS: TOPOLOGY, DYNAMICS AND SYNCHRONIZATION

2002 ◽  
Vol 12 (05) ◽  
pp. 885-916 ◽  
Author(s):  
XIAO FAN WANG
Keyword(s):  
Complex Networks ◽  
Network Models ◽  
Small World ◽  
Dynamical Networks ◽  
Scale Free ◽  
Epidemic Dynamics ◽  
The Past ◽  
The Relationship

Dramatic advances in the field of complex networks have been witnessed in the past few years. This paper reviews some important results in this direction of rapidly evolving research, with emphasis on the relationship between the dynamics and the topology of complex networks. Basic quantities and typical examples of various complex networks are described; and main network models are introduced, including regular, random, small-world and scale-free models. The robustness of connectivity and the epidemic dynamics in complex networks are also evaluated. To that end, synchronization in various dynamical networks are discussed according to their regular, small-world and scale-free connections.

Joint Combat System of Systems Modeling and Effectiveness Analysis Based on Complex Networks

2012 ◽  
Vol 591-593 ◽  
pp. 1589-1592 ◽  
Author(s):  
Yan Bo Qi ◽  
Liu Zhong ◽  
Le Zhang ◽  
Jiang Hu Xu
Keyword(s):  
Complex Networks ◽  
Network Models ◽  
System Of Systems ◽  
Clustering Coefficient ◽  
Network Effect ◽  
Scale Free ◽  
Effectiveness Analysis ◽  
Joint Operations ◽  
The Difference ◽  
Basic Network

How to describe the difference among various combat networks and measure their effectiveness is an important problem in combat analysis. In this paper three basic network models are developed based on the theory of complex networks and a new method is put forward for measuring the network effect of combat SoS. Numerical comparisons of the three combat network models indicate that though integrated joint operations network has the highest networked effects in networked effectiveness and clustering coefficient, but when considering the Average Path Length index, it has the lowest effectiveness. The results also suggest that the degree distribution of integrated joint operations network is scale-free thus it has the highest survivability.

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 SMALL-WORLD PROPERTY IN NETWORKS GROWING BY ACTIVE EDGES

2011 ◽  
Vol 14 (06) ◽  
pp. 853-869 ◽  
Author(s):  
PHILIPPE J. GIABBANELLI
Keyword(s):  
Growth Mechanism ◽  
Average Distance ◽  
Network Models ◽  
Small World ◽  
Clustering Coefficient ◽  
Small World Networks ◽  
Fractal Approach ◽  
Small World Property ◽  
Complex Network Models ◽  
Similar Growth

In the last three years, we have witnessed an increasing number of complex network models based on a 'fractal' approach, in which parts of the network are repeatedly replaced by a given pattern. Our focus is on models that can be defined by repeatedly adding a pattern network to selected edges, called active edges. We prove that when a pattern network has at least two active edges, then the resulting network has an average distance at most logarithmic in the number of nodes. This suggests that real-world networks based on a similar growth mechanism are likely to have small average distance. We provide an estimate of the clustering coefficient and verify its accuracy using simulations. Using numerous examples of simple patterns, our simulations show various ways to generate small-world networks. Finally, we discuss extensions to our framework encompassing probabilistic patterns and active subnetworks.

scholarly journals Small-World and Scale-Free Network Models for IoT Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Insoo Sohn
Keyword(s):  
Graph Theory ◽  
Complex Network ◽  
Network Topology ◽  
Network Models ◽  
Small World ◽  
Small World Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
Massive Number ◽  
Complex Network Models

It is expected that Internet of Things (IoT) revolution will enable new solutions and business for consumers and entrepreneurs by connecting billions of physical world devices with varying capabilities. However, for successful realization of IoT, challenges such as heterogeneous connectivity, ubiquitous coverage, reduced network and device complexity, enhanced power savings, and enhanced resource management have to be solved. All these challenges are heavily impacted by the IoT network topology supported by massive number of connected devices. Small-world networks and scale-free networks are important complex network models with massive number of nodes and have been actively used to study the network topology of brain networks, social networks, and wireless networks. These models, also, have been applied to IoT networks to enhance synchronization, error tolerance, and more. However, due to interdisciplinary nature of the network science, with heavy emphasis on graph theory, it is not easy to study the various tools provided by complex network models. Therefore, in this paper, we attempt to introduce basic concepts of graph theory, including small-world networks and scale-free networks, and provide system models that can be easily implemented to be used as a powerful tool in solving various research problems related to IoT.

scholarly journals Modeling Complex Networks Based on Deep Reinforcement Learning

2022 ◽  
Vol 9 ◽  
Author(s):  
Wenbo Song ◽  
Wei Sheng ◽  
Dong Li ◽  
Chong Wu ◽  
Jun Ma
Keyword(s):  
Reinforcement Learning ◽  
Complex Networks ◽  
Network Topology ◽  
Network Structure ◽  
Dynamic Change ◽  
Intelligent Agent ◽  
Small World ◽  
Network Nodes ◽  
Scale Free ◽  
Internal Mechanism

The network topology of complex networks evolves dynamically with time. How to model the internal mechanism driving the dynamic change of network structure is the key problem in the field of complex networks. The models represented by WS, NW, BA usually assume that the evolution of network structure is driven by nodes’ passive behaviors based on some restrictive rules. However, in fact, network nodes are intelligent individuals, which actively update their relations based on experience and environment. To overcome this limitation, we attempt to construct a network model based on deep reinforcement learning, named as NMDRL. In the new model, each node in complex networks is regarded as an intelligent agent, which reacts with the agents around it for refreshing its relationships at every moment. Extensive experiments show that our model not only can generate networks owing the properties of scale-free and small-world, but also reveal how community structures emerge and evolve. The proposed NMDRL model is helpful to study propagation, game, and cooperation behaviors in networks.

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