scholarly journals Disparity of clustering coefficients in the Holme‒Kim network model

2018 ◽  
Vol 50 (3) ◽  
pp. 918-943
Author(s):  
R. I. Oliveira ◽  
R. Ribeiro ◽  
R. Sanchis
Keyword(s):  
Random Graph ◽  
Network Model ◽  
Slow Rate ◽  
Clustering Coefficient ◽  
Concentration Inequality ◽  
Free Graph ◽  
Scale Free ◽  
Local Clustering ◽  
Clustering Coefficients ◽  
Local Clustering Coefficient

Abstract The Holme‒Kim random graph process is a variant of the Barabási‒Álbert scale-free graph that was designed to exhibit clustering. In this paper we show that whether the model does indeed exhibit clustering depends on how we define the clustering coefficient. In fact, we find that the local clustering coefficient typically remains positive whereas global clustering tends to 0 at a slow rate. These and other results are proven via martingale techniques, such as Freedman's concentration inequality combined with a bootstrapping argument.

scholarly journals Ordered increasing $k$-trees: Introduction and analysis of a preferential attachment network model

2010 ◽  
Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽  
Author(s):  
Alois Panholzer ◽  
Georg Seitz
Keyword(s):  
Network Model ◽  
Preferential Attachment ◽  
Graph Model ◽  
Clustering Coefficient ◽  
Tree Model ◽  
Random Graph Model ◽  
Local Clustering ◽  
Tree Models ◽  
International Audience ◽  
Local Clustering Coefficient

International audience We introduce a random graph model based on $k$-trees, which can be generated by applying a probabilistic preferential attachment rule, but which also has a simple combinatorial description. We carry out a precise distributional analysis of important parameters for the network model such as the degree, the local clustering coefficient and the number of descendants of the nodes and root-to-node distances. We do not only obtain results for random nodes, but in particular we also get a precise description of the behaviour of parameters for the $j$-th inserted node in a random $k$-tree of size $n$, where $j=j(n)$ might grow with $n$. The approach presented is not restricted to this specific $k$-tree model, but can also be applied to other evolving $k$-tree models.

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.

Words, constructions and corpora: Network representations of constructional semantics for Mandarin space particles

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Alvin Cheng-Hsien Chen
Keyword(s):  
Clustering Coefficient ◽  
Linguistic Knowledge ◽  
Scale Free ◽  
Network Analyses ◽  
Semantic Fields ◽  
Text Corpora ◽  
Quantitative Properties ◽  
Local Clustering Coefficient ◽  
Linguistic Units

AbstractIn this study, we aim to demonstrate the effectiveness of network science in exploring the emergence of constructional semantics from the connectedness and relationships between linguistic units. With Mandarin locative constructions (MLCs) as a case study, we extracted constructional tokens from a representative corpus, including their respective space particles (SPs) and the head nouns of the landmarks (LMs), which constitute the nodes of the network. We computed edges based on the lexical similarities of word embeddings learned from large text corpora and the SP-LM contingency from collostructional analysis. We address three issues: (1) For each LM, how prototypical is it of the meaning of the SP? (2) For each SP, how semantically cohesive are its LM exemplars? (3) What are the emerging semantic fields from the constructional network of MLCs? We address these questions by examining the quantitative properties of the network at three levels: microscopic (i.e., node centrality and local clustering coefficient), mesoscopic (i.e., community) and macroscopic properties (i.e., small-worldness and scale-free). Our network analyses bring to the foreground the importance of repeated language experiences in the shaping and entrenchment of linguistic knowledge.

Survivability of public transit network based on network structure entropy

2015 ◽  
Vol 26 (09) ◽  
pp. 1550104 ◽  
Author(s):  
Bai-Bai Fu ◽  
Lin Zhang ◽  
Shu-Bin Li ◽  
Yun-Xuan Li
Keyword(s):  
Network Model ◽  
Network Structure ◽  
Public Transit ◽  
Small World ◽  
Clustering Coefficient ◽  
Statistical Characteristics ◽  
Network Efficiency ◽  
Transit Network ◽  
Scale Free ◽  
The Public

In this work, we have collected 195 bus routes and 1433 bus stations of Jinan city as sample date to build up the public transit geospatial network model by applying space L method, until May 2014. Then, by analyzing the topological properties of public transit geospatial network model, which include degree and degree distribution, average shortest path length, clustering coefficient and betweenness, we get the conclusion that public transit network is a typical complex network with scale-free and small-world characteristics. Furthermore, in order to analyze the survivability of public transit network, we define new network structure entropy based on betweenness importance, and prove its correctness by giving that the new network structure entropy has the same statistical characteristics with network efficiency. Finally, the "inflexion zone" is discovered, which can be taken as the momentous indicator to determine the public transit network failure.

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.

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.

scholarly journals Closure coefficients in scale-free complex networks

2020 ◽  
Vol 8 (3) ◽  
Author(s):  
Clara Stegehuis
Keyword(s):  
Complex Networks ◽  
Random Graph ◽  
Clustering Coefficient ◽  
Graph Models ◽  
Variable Model ◽  
Scale Free ◽  
Random Graph Models ◽  
Local Closure ◽  
Head Node ◽  
High Degree

Abstract The formation of triangles in complex networks is an important network property that has received tremendous attention. The formation of triangles is often studied through the clustering coefficient. The closure coefficient or transitivity is another method to measure triadic closure. This statistic measures clustering from the head node of a triangle (instead of from the centre node, as in the often studied clustering coefficient). We perform a first exploratory analysis of the behaviour of the local closure coefficient in two random graph models that create simple networks with power-law degrees: the hidden-variable model and the hyperbolic random graph. We show that the closure coefficient behaves significantly different in these simple random graph models than in the previously studied multigraph models. We also relate the closure coefficient of high-degree vertices to the clustering coefficient and the average nearest neighbour degree.

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