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.

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.

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.

A NETWORK MODEL GENERATED FROM THE RECURSIVE GRAPH BASED ON POLYGON

2013 ◽  
Vol 24 (09) ◽  
pp. 1350062 ◽  
Author(s):  
YUANYUAN SUN ◽  
KAINING HOU ◽  
YUJIE ZHAO
Keyword(s):  
Real Life ◽  
Network Models ◽  
Small World ◽  
Mapping Method ◽  
Clustering Coefficient ◽  
Research Fields ◽  
Network Diameter ◽  
Degree Correlations ◽  
New Perspective ◽  
Small World Property

The study of network models is one of the most challenging research fields among the studies of complex networks, which have been the hot research topics in recent decades. In this paper, we construct a deterministic network by a mapping method based on a recursive graph, and analyze its topological characteristics, including degree distribution, clustering coefficient, network diameter, average path length and degree correlations. We obtain that this network has the small-world property and positive correlation. The network modeling as we present gives a new perspective on networks, and helps to understand better the evolutions of the real-life systems, making it possible to explore the complexity of complex systems.

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.

STOCHASTIC EVOLVING MODEL FOR COMPLEX NETWORKS

2004 ◽  
Vol 18 (23) ◽  
pp. 1157-1164 ◽  
Author(s):  
HYUN-JOO KIM ◽  
YEON-MU CHOI ◽  
JIN MIN KIM
Keyword(s):  
Control Parameter ◽  
Small World ◽  
Network Size ◽  
Clustering Coefficient ◽  
Scale Free ◽  
Hierarchical Topology ◽  
Free Behavior ◽  
Small World Property ◽  
Evolving Model ◽  
High Degree

We introduce an evolving complex network model, where a new vertex is added and new edges between already existing vertices are added with a control parameter p. The model shows the characteristics of real networks such as small-world property, high degree of clustering, scale-free behavior in degree distribution, and hierarchical topology. We obtain the various values of degree exponent γ in the range 2<γ≤3 by adjusting the parameter p and find that the degree exponent decreases logarithmically with p. In addition, the clustering coefficient is tunable by changing the control parameter p, and the average path length L is proportional to ln ( ln N) with nonzero p, where N is the network size.

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.

Evolving complex networks with logistic property: Global versus local growth

2021 ◽  
Vol 35 (24) ◽  
Author(s):  
Sen Qin ◽  
Sha Peng
Keyword(s):  
Shortest Paths ◽  
Network Models ◽  
Logistic Growth ◽  
Scale Free Network ◽  
Network Growth ◽  
Network Nodes ◽  
Scale Free ◽  
Free Network ◽  
Law Degree ◽  
Global And Local

Considering the retarding effect of natural resources, environmental conditions, and other factors on network growth, the capacity of network nodes to connect to new edges is generally limited. Inspired by this hindered growth of many real-world networks, two types of evolving network models are suggested with different logistic growth schemes. In the global and local logistic network, the total number of network edges and the number of edges added into the network at each step are in line with the Logistic growth, respectively. The most exciting feature of the Logistic growth network is that the growth rule of network edges is first fast, then slow and finally reaches the saturation value [Formula: see text]. Theoretical analysis and numerical simulation reveal that the node degrees of two new networks converge to the same results of the BA scale-free network, [Formula: see text], as the growth rate [Formula: see text] approaches to 0. The local logistic network follows a bilateral power-law degree distribution with a given value of [Formula: see text]. Meanwhile, for these two networks, it is found that the greater [Formula: see text] and [Formula: see text], the smaller the average shortest paths, the greater the clustering coefficients, and the weaker the disassortativity. Additionally, compared to the local logistic growth network, the clustering feature of the global logistic network is more obvious.

scholarly journals VORONOI AND FRACTAL COMPLEX NETWORKS AND THEIR CHARACTERIZATION

2004 ◽  
Vol 15 (01) ◽  
pp. 175-183 ◽  
Author(s):  
LUCIANO DA FONTOURA COSTA
Keyword(s):  
Complex Networks ◽  
Metric Spaces ◽  
Spatial Scales ◽  
Shortest Paths ◽  
Network Models ◽  
Small World ◽  
Effective Length ◽  
Scale Free ◽  
Fractal Network ◽  
Natural Means

Real world networks are often characterized by spatial constraints such as the relative position and adjacency of nodes. The present work describes how Voronoi tessellations of the space where the network is embedded provide not only a natural means for relating such networks with metric spaces, but also a natural means for obtaining fractal complex networks. A series of comprehensive measurements closely related to spatial aspects of these networks is proposed, which includes the effective length, adjacency, as well as the fractal dimension of the network in terms of the spatial scales defined by successive shortest paths starting from a specific node. The potential of such features is illustrated with respect to the random, small-world, scale-free and fractal network models.

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.

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