A Clustering Coefficient Preference Model on Scale-free Networks

2012 ◽  
Vol 7 (4) ◽  
pp. 231-237
Author(s):  
You Li ◽  
Siqing Shan ◽  
Lu Liu
Keyword(s):  
Clustering Coefficient ◽  
Preference Model ◽  
Scale Free ◽  
Scale Free Networks

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 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.

Scale-free networks of the earth’s surface

2016 ◽  
Vol 30 (21) ◽  
pp. 1650143 ◽  
Author(s):  
Gang Liu ◽  
Jing He ◽  
Kaitian Luo ◽  
Peichao Gao ◽  
Lei Ma
Keyword(s):  
Structural Complexity ◽  
Google Earth ◽  
Living Environment ◽  
Clustering Coefficient ◽  
Science And Engineering ◽  
Scale Free ◽  
The Earth ◽  
Scale Free Networks ◽  
Power Law Distributions ◽  
Real Complex

Studying the structure of real complex systems is of paramount importance in science and engineering. Despite our understanding of lots of real systems, we hardly cognize our unique living environment — the earth. The structural complexity of the earth’s surface is, however, still unknown in detail. Here, we define the modeling of graph topology for the earth’s surface, using the satellite images of the earth’s surface under different spatial resolutions derived from Google Earth. We find that the graph topologies of the earth’s surface are scale-free networks regardless of the spatial resolutions. For different spatial resolutions, the exponents of power-law distributions and the modularity are both quite different; however, the average clustering coefficient is approximately equal to a constant. We explore the morphology study of the earth’s surface, which enables a comprehensive understanding of the morphological feature of the earth’s surface.

scholarly journals STRUCTURAL EFFECTS ON SYNCHRONIZABILITY OF SCALE-FREE NETWORKS

2008 ◽  
Vol 19 (09) ◽  
pp. 1359-1366 ◽  
Author(s):  
JIAN-GUO LIU ◽  
TAO ZHOU ◽  
QIANG GUO ◽  
BING-HONG WANG
Keyword(s):  
Tabu Search ◽  
Optimal Algorithm ◽  
Structural Characteristics ◽  
Degree Sequence ◽  
Reduction Process ◽  
Clustering Coefficient ◽  
Structural Effects ◽  
Exchange Method ◽  
Scale Free ◽  
Scale Free Networks

In this paper, we numerically investigate the structural characteristics that affect the synchronizability of coupled identical oscillators on scale-free networks. By using the edge-exchange method, we can change the network structure with degree sequence fixed. An optimal algorithm, namely Tabu Search, is applied, respectively, to enhance and weaken the synchronizability. The numerical results indicate that the synchronizability is most sensitive to the maximal betweenness. By tracking the optimization process, most previous works suggest that the synchonizability can be enhanced by reducing assortative coefficient and clustering coefficient; however, interestingly, our numerical simulations show that the depression of synchronizability also corresponds to the reduction process of those two coefficients.

scholarly journals The Architecture of Complex Systems

2004 ◽  
Author(s):  
Vito Latora ◽  
Massimo Marchiori
Keyword(s):  
Complex System ◽  
Statistical Physics ◽  
Social Systems ◽  
Clustering Coefficient ◽  
Characteristic Path Length ◽  
Scale Free ◽  
Completely Regular ◽  
Scale Free Networks ◽  
Nonextensive Thermodynamics ◽  
Definition Of

At the present time, the most commonly accepted definition of a complex system is that of a system containing many interdependent constituents which interact nonlinearly. Therefore, when we want to model a complex system, the first issue has to do with the connectivity properties of its network, the architecture of the wirings between the constituents. In fact, we have recently learned that the network structure can be as important as the nonlinear interactions between elements, and an accurate description of the coupling architecture and a characterization of the structural properties of the network can be of fundamental importance also in understanding the dynamics of the system. In the last few years the research on networks has taken different directions producing rather unexpected and important results. Researchers have: (1) proposed various global variables to describe and characterize the properties of realworld networks and (2) developed different models to simulate the formation and the growth of networks such as the ones found in the real world. The results obtained can be summed up by saying that statistical physics has been able to capture the structure of many diverse systems within a few common frameworks, though these common frameworks are very different from the regular array, or capture the random connectivity, previously used to model the network of a complex system. Here we present a list of some of the global quantities introduced to characterize a network: the characteristic path length L, the clustering coefficient C, the global efficiency E<sub>glob</sub>, the local efficiency E<sub>loc</sub>, the cost Cost, and the degree distribution P(k). We also review two classes of networks proposed: smallworld and scale-free networks. We conclude with a possible application of the nonextensive thermodynamics formalism to describe scale-free networks. Watts and Strogatz [17] have shown that the connection topology of some biological, social, and technological networks is neither completely regular nor completely random. These networks, that are somehow in between regular and random networks, have been named small worlds in analogy with the smallworld phenomenon empirically observed in social systems more than 30 years ago [11, 12].

Tolerance analysis in scale-free social networks with varying degree exponents

2019 ◽  
Vol 37 (1) ◽  
pp. 57-71 ◽  
Author(s):  
Kwok Tai Chui ◽  
Chien-wen Shen
Keyword(s):  
Social Networks ◽  
Tolerance Analysis ◽  
Network Size ◽  
Average Density ◽  
Clustering Coefficient ◽  
Node Degree ◽  
User Requirement ◽  
Content Type ◽  
Scale Free ◽  
Scale Free Networks

Purpose There are many complex networks like World-Wide Web, internet and social networks have been reported to be scale-free. The major property of scale-free networks is their degree distributions are in power law form. Generally, the degree exponents of scale-free networks fall into the range of (2, 3). The purpose of this paper is to investigate other situations where the degree exponents may lie outside the range. Design/methodology/approach In this paper, analysis has been carried out by varying the degree exponents in the range of (0.5, 4.5). In total, 243 scenarios have been generated with varying network size of 1,000, 2,000 and 4,000, and degree exponents in the range of (0.5, 4.5) using interval of 0.05. Findings The following five indicators have been investigated: average density, average clustering coefficient, average path length, average diameter and average node degree. These indicators vary with the network size and degree exponent. If certain indicators do not satisfy with the user requirement using degree exponents of (2, 3), one can further increase or decrease the value with tradeoff. Results recommend that for degree exponents in (0.5, 2), 26 possible scale-free networks can be selected whereas for (3, 4.5), 41 possible scale-free networks can be selected, assuming a 100 percent deviation on the network parameters. Originality/value A tolerance analysis is given for the tradeoff and guideline is drawn to help better design of scale-free network for degree exponents in range of (0.5, 2) and (3, 4.5) using network size 1,000, 2,000 and 4,000. The methodology is applicable to any network size.

scholarly journals Analysis and synthesis of a growing network model generating dense scale-free networks via category theory

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Taichi Haruna ◽  
Yukio-Pegio Gunji
Keyword(s):  
Network Model ◽  
Category Theory ◽  
Clustering Coefficient ◽  
Scale Free ◽  
Degree Correlation ◽  
Proposed Model ◽  
Scale Free Networks ◽  
Analysis And Synthesis ◽  
Local Clustering Coefficient ◽  
Growing Network

AbstractWe propose a growing network model that can generate dense scale-free networks with an almost neutral degree−degree correlation and a negative scaling of local clustering coefficient. The model is obtained by modifying an existing model in the literature that can also generate dense scale-free networks but with a different higher-order network structure. The modification is mediated by category theory. Category theory can identify a duality structure hidden in the previous model. The proposed model is built so that the identified duality is preserved. This work is a novel application of category theory for designing a network model focusing on a universal algebraic structure.

Sign in / Sign up

Export Citation Format

Share Document