scholarly journals Dense Networks With Mixture Degree Distribution

2021 ◽  
Vol 9 ◽  
Author(s):  
Xiaomin Wang ◽  
Fei Ma ◽  
Bing Yao
Keyword(s):  
Complex Networks ◽  
Degree Distribution ◽  
Metabolic Networks ◽  
First Passage Time ◽  
Small World ◽  
Passage Time ◽  
Friendship Networks ◽  
Scale Free ◽  
Dense Networks ◽  
Protein Protein Interaction

Complex networks have become a powerful tool to describe the structure and evolution in a large quantity of real networks in the past few years, such as friendship networks, metabolic networks, protein–protein interaction networks, and software networks. While a variety of complex networks have been published, dense networks sharing remarkable structural properties, such as the scale-free feature, are seldom reported. Here, our goal is to construct a class of dense networks. Then, we discover that our networks follow the mixture degree distribution; that is, there is a critical point above which the cumulative degree distribution has a power-law form and below which the exponential distribution is observed. Next, we also prove the networks proposed to show the small-world property. Finally, we study random walks on our networks with a trap fixed at a vertex with the highest degree and find that the closed form for the mean first-passage time increases logarithmically with the number of vertices of our networks.

One-Step Memory Random Walk on Complex Networks: An Efficient Local Navigation Strategy

2021 ◽  
pp. 2150040
Author(s):  
Xinxin Cao ◽  
Yan Wang ◽  
Cheng Li ◽  
Tongfeng Weng ◽  
Huijie Yang ◽  
...  
Keyword(s):  
Random Walk ◽  
Complex Networks ◽  
First Passage Time ◽  
Network Models ◽  
Small World ◽  
Passage Time ◽  
Time Step ◽  
Biased Random Walk ◽  
Navigation Strategy ◽  
One Step

We propose one-step memory random walk on complex networks for which at each time step, the walker will not be allowed to revisit the last position. Mean first passage time is adopted to quantify its search efficiency and a procedure is provided for calculating it analytically. Interestingly, we find that in the same circumstance, one-step memory random walk usually takes less time than random walk for finding a target given in advance. Furthermore, this navigation strategy presents a better performance even in comparison with corresponding optimal biased random walk when moving on networks without small-world effect. Our findings are confirmed on two canonical network models and a number of real networks. Our work reveals that one-step memory random walk is an efficient local search strategy, which can be applied to transportation and information spreading.

scholarly journals Polygon-Based Hierarchical Planar Networks Based on Generalized Apollonian Construction

Physics ◽  
2021 ◽  
Vol 3 (4) ◽  
pp. 998-1014
Author(s):  
Mikhail Tamm ◽  
Dmitry Koval ◽  
Vladimir Stadnichuk
Keyword(s):  
Complex Networks ◽  
Power Law ◽  
Degree Distribution ◽  
Small World ◽  
Scale Free ◽  
Model Network ◽  
Suggested Procedure ◽  
Similar Construction ◽  
Scale Free Graphs ◽  
Planar Networks

Experimentally observed complex networks are often scale-free, small-world and have an unexpectedly large number of small cycles. An Apollonian network is one notable example of a model network simultaneously having all three of these properties. This network is constructed by a deterministic procedure of consequentially splitting a triangle into smaller and smaller triangles. In this paper, a similar construction based on the consequential splitting of tetragons and other polygons with an even number of edges is presented. The suggested procedure is stochastic and results in the ensemble of planar scale-free graphs. In the limit of a large number of splittings, the degree distribution of the graph converges to a true power law with an exponent, which is smaller than three in the case of tetragons and larger than three for polygons with a larger number of edges. It is shown that it is possible to stochastically mix tetragon-based and hexagon-based constructions to obtain an ensemble of graphs with a tunable exponent of degree distribution. Other possible planar generalizations of the Apollonian procedure are also briefly 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.

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.

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.

The Research of Complex Network on Archives Blog

2011 ◽  
Vol 181-182 ◽  
pp. 14-18
Author(s):  
Yi He
Keyword(s):  
Information Sharing ◽  
Complex Network ◽  
Network Model ◽  
Degree Distribution ◽  
Small World ◽  
Scale Free ◽  
Set Up

At the background of archives blog on Internet, this paper constructs a directed complex network model, and analyzes the network characters such as degree distribution. To verify its efficiency, we collect blogs’ information and set up a complex network..From the analysis result of the simulation and demonstration network, we know that they have the same characters, which show that, the virtual society network has small-world effect and scale-free character compared with real society network. The results indicate that the establishment of archives blog is favor to spread rapidly archives information, improve information sharing efficiency and promote the development of archives technology.

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.

TRAFFIC CONGESTION ANALYSIS IN COMPLEX NETWORKS BASED ON VARIOUS ROUTING STRATEGIES

2007 ◽  
Vol 21 (15) ◽  
pp. 929-939 ◽  
Author(s):  
XUAN GUO ◽  
HONGTAO LU
Keyword(s):  
Complex Networks ◽  
Traffic Congestion ◽  
Small World ◽  
Modern Society ◽  
Information Communication ◽  
Shortest Path Routing ◽  
Scale Free ◽  
Deterministic Routing ◽  
Routing Strategy ◽  
Network Topologies

Networks, acting as infrastructure for information communication, play an important role in modern society, therefore, the elements affecting the efficiency of network traffic are worthy of deep research. In this paper, we investigate numerically the problem of traffic congestion in complex networks through the use of various routing strategies. Three types of complex networks structures, namely Poisson random networks, small-world networks and scale-free networks, are considered. Three different routing strategies are used on networks: deterministic routing strategy, preferential routing strategy and shortest path routing strategy. We evaluate the efficiency of different routing strategies on different network topologies and show how the network structures and routing strategies influence the traffic congestion status.

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