scholarly journals Random intersection graphs with communities

2021 ◽  
Vol 53 (4) ◽  
pp. 1061-1089
Author(s):  
Remco van der Hofstad ◽  
Júlia Komjáthy ◽  
Viktória Vadon
Keyword(s):  
Weak Convergence ◽  
Internal Structure ◽  
Degree Distribution ◽  
Clustering Coefficient ◽  
Intersection Graphs ◽  
Structure Of Communities ◽  
Local Clustering ◽  
Model Networks ◽  
Local Weak Convergence ◽  
Local Clustering Coefficient

AbstractRandom intersection graphs model networks with communities, assuming an underlying bipartite structure of communities and individuals, where these communities may overlap. We generalize the model, allowing for arbitrary community structures within the communities. In our new model, communities may overlap, and they have their own internal structure described by arbitrary finite community graphs. Our model turns out to be tractable. We analyze the overlapping structure of the communities, show local weak convergence (including convergence of subgraph counts), and derive the asymptotic degree distribution and the local clustering coefficient.

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 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 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 Examining association between cohesion and diversity in collaboration networks of pharmaceutical clinical trials with drug approvals

2020 ◽  
Author(s):  
Gary Lin ◽  
Sauleh Siddiqui ◽  
Jen Bernstein ◽  
Diego A Martinez ◽  
Lauren Gardner ◽  
...  
Keyword(s):  
Clinical Trials ◽  
Organizational Behavior ◽  
Nonprofit Organizations ◽  
Clustering Coefficient ◽  
Collaboration Network ◽  
Pharmaceutical Companies ◽  
Public Consumption ◽  
Local Clustering ◽  
Negative Effect ◽  
Local Clustering Coefficient

Abstract Objective Clinical trials ensure that pharmaceutical treatments are safe, efficacious, and effective for public consumption, but are extremely complex, taking up to 10 years and $2.6 billion to complete. One main source of complexity arises from the collaboration between actors, and network science methodologies can be leveraged to explore that complexity. We aim to characterize collaborations between actors in the clinical trials context and investigate trends of successful actors. Materials and Methods We constructed a temporal network of clinical trial collaborations between large and small-size pharmaceutical companies, academic institutions, nonprofit organizations, hospital systems, and government agencies from public and proprietary data and introduced metrics to quantify actors’ collaboration network structure, organizational behavior, and partnership characteristics. A multivariable regression analysis was conducted to determine the metrics’ relationship with success. Results We found a positive correlation between the number of successful approved trials and interdisciplinary collaborations measured by a collaboration diversity metric (P < .01). Our results also showed a negative effect of the local clustering coefficient (P < .01) on the success of clinical trials. Large pharmaceutical companies have the lowest local clustering coefficient and more diversity in partnerships across biomedical specializations. Conclusions Large pharmaceutical companies are more likely to collaborate with a wider range of actors from other specialties, especially smaller industry actors who are newcomers in clinical research, resulting in exclusive access to smaller actors. Future investigations are needed to show how concentrations of influence and resources might result in diminished gains in treatment development.

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