scholarly journals Characterizing several properties of high-dimensional random Apollonian networks

2020 ◽  
Vol 8 (4) ◽  
Author(s):  
Panpan Zhang
Keyword(s):  
Small World ◽  
Wiener Index ◽  
Clustering Coefficient ◽  
Probabilistic Methods ◽  
High Dimensional ◽  
Analytic Combinatorics ◽  
Local Clustering ◽  
Clustering Property ◽  
Small World Property ◽  
Local Clustering Coefficient

Abstract In this article, we investigate several properties of high-dimensional random Apollonian networks, including two types of degree profiles, the small-world effect (clustering property), sparsity and three distance-based metrics. The characterizations of the degree profiles are based on several rigorous mathematical and probabilistic methods, such as a two-dimensional mathematical induction, analytic combinatorics and Pólya urns, etc. The small-world property is uncovered by a well-developed measure—local clustering coefficient and the sparsity is assessed by a proposed Gini index. Finally, we look into three distance-based properties; they are total depth, diameter and Wiener index.

scholarly journals Directed random geometric graphs

2019 ◽  
Vol 7 (5) ◽  
pp. 792-816
Author(s):  
Jesse Michel ◽  
Sushruth Reddy ◽  
Rikhav Shah ◽  
Sandeep Silwal ◽  
Ramis Movassagh
Keyword(s):  
Real World ◽  
Word Association ◽  
Graph Model ◽  
Small World ◽  
Geometric Graph ◽  
Clustering Coefficient ◽  
Random Geometric Graph ◽  
Random Geometric Graphs ◽  
Scale Free ◽  
Small World Property

Abstract Many real-world networks are intrinsically directed. Such networks include activation of genes, hyperlinks on the internet and the network of followers on Twitter among many others. The challenge, however, is to create a network model that has many of the properties of real-world networks such as power-law degree distributions and the small-world property. To meet these challenges, we introduce the Directed Random Geometric Graph (DRGG) model, which is an extension of the random geometric graph model. We prove that it is scale-free with respect to the indegree distribution, has binomial outdegree distribution, has a high clustering coefficient, has few edges and is likely small-world. These are some of the main features of aforementioned real-world networks. We also empirically observed that word association networks have many of the theoretical properties of the DRGG model.

scholarly journals Counting Triangles in Power-Law Uniform Random Graphs

10.37236/9239 ◽  
2020 ◽  
Vol 27 (3) ◽  
Author(s):  
Pu Gao ◽  
Remco Van der Hofstad ◽  
Angus Southwell ◽  
Clara Stegehuis
Keyword(s):  
Random Graphs ◽  
Power Law ◽  
Degree Sequence ◽  
Clustering Coefficient ◽  
Linear Functions ◽  
Configuration Model ◽  
Local Clustering ◽  
Asymptotic Number ◽  
Multiple Edges ◽  
Local Clustering Coefficient

We count the asymptotic number of triangles in uniform random graphs where the degree distribution follows a power law with degree exponent $\tau\in(2,3)$. We also analyze the local clustering coefficient $c(k)$, the probability that two random neighbors of a vertex of degree $k$ are connected. We find that the number of triangles, as well as the local clustering coefficient, scale similarly as in the erased configuration model, where all self-loops and multiple edges of the configuration model are removed. Interestingly, uniform random graphs contain more triangles than erased configuration models with the same degree sequence. The number of triangles in uniform random graphs is closely related to that in a version of the rank-1 inhomogeneous random graph, where all vertices are equipped with weights, and the probabilities that edges are present are moderated by asymptotically linear functions of the products of these vertex weights.

SMALL-WORLD EFFECT IN GEOGRAPHICAL ATTACHMENT NETWORKS

2019 ◽  
pp. 1-21
Author(s):  
Qunqiang Feng ◽  
Yongkang Wang ◽  
Zhishui Hu
Keyword(s):  
Network Model ◽  
Degree Distribution ◽  
Small World ◽  
Clustering Coefficient ◽  
Probabilistic Methods ◽  
Small World Network ◽  
Computational Simulations ◽  
Physical Literature

AbstractIn this work, we use rigorous probabilistic methods to study the asymptotic degree distribution, clustering coefficient, and diameter of geographical attachment networks. As a type of small-world network model, these networks were first proposed in the physical literature, where they were analyzed only with heuristic arguments and computational simulations.

A NEW DYNAMIC COMMUNITY MODEL FOR SOCIAL NETWORKS

2014 ◽  
Vol 25 (02) ◽  
pp. 1350088 ◽  
Author(s):  
ZHE-MING LU ◽  
ZHEN WU ◽  
SHI-ZE GUO ◽  
ZHE CHEN ◽  
GUANG-HUA SONG
Keyword(s):  
Social Networks ◽  
Average Distance ◽  
Small World ◽  
Clustering Coefficient ◽  
Community Model ◽  
Network Diameter ◽  
Proposed Model ◽  
Small World Property ◽  
Two Parameters ◽  
Dynamic Community

In this paper, based on the phenomenon that individuals join into and jump from the organizations in the society, we propose a dynamic community model to construct social networks. Two parameters are adopted in our model, one is the communication rate Pa that denotes the connection strength in the organization and the other is the turnover rate Pb, that stands for the frequency of jumping among the organizations. Based on simulations, we analyze not only the degree distribution, the clustering coefficient, the average distance and the network diameter but also the group distribution which is closely related to their community structure. Moreover, we discover that the networks generated by the proposed model possess the small-world property and can well reproduce the networks of social contacts.

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.

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.

scholarly journals Overlapping Structures Detection in Protein-Protein Interaction Networks Using Community Detection Algorithm Based on Neighbor Clustering Coefficient

2021 ◽  
Vol 12 ◽  
Author(s):  
Yan Wang ◽  
Chen Qiong ◽  
Lili Yang ◽  
Sen Yang ◽  
Kai He ◽  
...  
Keyword(s):  
Community Detection ◽  
Detection Algorithm ◽  
Clustering Coefficient ◽  
Functional Modules ◽  
Seed Selection ◽  
Protein Protein Interaction ◽  
Ppi Networks ◽  
Local Clustering ◽  
Community Detection Algorithm ◽  
Local Clustering Coefficient

With the rapid development of bioinformatics, researchers have applied community detection algorithms to detect functional modules in protein-protein interaction (PPI) networks that can predict the function of unknown proteins at the molecular level and further reveal the regularity of cell activity. Clusters in a PPI network may overlap where a protein is involved in multiple functional modules. To identify overlapping structures in protein functional modules, this paper proposes a novel overlapping community detection algorithm based on the neighboring local clustering coefficient (NLC). The contributions of the NLC algorithm are threefold: (i) Combine the edge-based community detection method with local expansion in seed selection and the local clustering coefficient of neighboring nodes to improve the accuracy of seed selection; (ii) A method of measuring the distance between edges is improved to make the result of community division more accurate; (iii) A community optimization strategy for the excessive overlapping nodes makes the overlapping structure more reasonable. The experimental results on standard networks, Lancichinetti-Fortunato-Radicchi (LFR) benchmark networks and PPI networks show that the NLC algorithm can improve the Extended modularity (EQ) value and Normalized Mutual Information (NMI) value of the community division, which verifies that the algorithm can not only detect reasonable communities but also identify overlapping structures in networks.

scholarly journals Structure and Evolution of the International Pesticide Trade Networks

2021 ◽  
Vol 9 ◽  
Author(s):  
Jian-An Li ◽  
Wen-Jie Xie ◽  
Wei-Xing Zhou
Keyword(s):  
International Trade ◽  
Dynamic Properties ◽  
Network Size ◽  
Clustering Coefficient ◽  
Trade Networks ◽  
The World ◽  
Local Clustering ◽  
Increasing Demand ◽  
Positive Correlations ◽  
Local Clustering Coefficient

To meet the increasing demand for food around the world, pesticides are widely used and will continue to be widely used in agricultural production to reduce yield losses and maintain product quality. International pesticide trade serves to reallocate the distribution of pesticides around the world. We investigate the statistical properties of the international trade networks of five categories of pesticides from the view angle of temporal directed and weighted networks. We observed an overall increasing trend in network size, network density, average in- and out-degrees, average in- and out-strengths, temporal similarity, and link reciprocity, indicating that the rising globalization of pesticides trade is driving the networks denser. However, the distributions of link weights remain unchanged along time for the five categories of pesticides. In addition, all the networks are disassortatively mixed because large importers or exporters are more likely to trade with small exporters or importers. We also observed positive correlations between in-degree and out-degree, in-strength and out-strength, link reciprocity and in-degree, out-degree, in-strength, and out-strength, while node’s local clustering coefficient is negatively related to in-degree, out-degree, in-strength, and out-strength. We show that some structural and dynamic properties of the international pesticide trade networks are different from those of the international trade networks, highlighting the presence of idiosyncratic features of different goods and products in the international trade.

Abstract 663: Metabolomics And Correlation Network Analysis Of Hypertension

Hypertension ◽  
2014 ◽  
Vol 64 (suppl_1) ◽  
Author(s):  
zhongmin tian ◽  
le wang ◽  
entai hou ◽  
qiong sun
Keyword(s):  
Amino Acids ◽  
Comprehensive Evaluation ◽  
Small World ◽  
Clustering Coefficient ◽  
Correlation Network ◽  
Beta Alanine ◽  
Topological Parameters ◽  
Correlation Networks ◽  
Metabolomics Study ◽  
Small World Property

The awareness, treatment and controls rates of hypertension for people in their 20s and 30s age are much lower than average. In this paper, a GC/MS based metabolomics study was performed in plasma of young hypertensive men and age-matched normal ones. Correlations of the identified metabolites were analyzed and visualized. A systematic correlation network was constructed with the significance of correlation coefficient setting at threshold of 0.6. Glycine, lysine, cystine and beta-alanine were selected as the most important nodes of the network, with high values of degree. A relatively short average path length and high clustering coefficient suggested a small-world property of the network. Moreover, differential metabolites in young hypertensive men were used to construct a core correlation network for further understanding. Four hubs (lysine, glycine, cystine and tryptophan) were confirmed by a comprehensive evaluation of three centrality indices. The statistical and topological parameters of the network indicated that local disturbance to hubs would rapidly transfer to the whole network. These results demonstrated that the distinct metabolic profiles of young hypertensive men might be due to perturbation of the biosynthesis pathway of amino acids. Integrated analyses of metabolomics and correlation networks would provide a broadened window for further understanding of hypertension. Key Words: metabolomics; hypertension; correlation network; amino acids; statistical and topological characteristics; centrality indices; hubs

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