scholarly journals Clustering coefficient of random intersection graphs with infinite degree variance

2016 ◽  
pp. 0-0
Author(s):  
Mindaugas Bloznelis ◽  
Valentas Kurauskas
Keyword(s):  
Clustering Coefficient ◽  
Intersection Graphs ◽  
Degree Variance ◽  
Infinite Degree

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.

ANALISIS PERINGKAT TOP BRAND OJEK ONLINE MENGGUNAKAN JEJARING SOSIAL PERCAKAPAN TWITTER

2019 ◽  
Vol 24 (2) ◽  
pp. 88-104
Author(s):  
Ilham Aminudin ◽  
Dyah Anggraini
Keyword(s):  
Social Media ◽  
Social Network ◽  
Social Network Analysis ◽  
Network Analysis ◽  
Path Length ◽  
Average Path Length ◽  
Average Degree ◽  
Clustering Coefficient ◽  
R Programming

Banyak bisnis mulai muncul dengan melibatkan pengembangan teknologi internet. Salah satunya adalah bisnis di aplikasi berbasis penyedia layanan di bidang moda transportasi berbasis online yang ternyata dapat memberikan solusi dan menjawab berbagai kekhawatiran publik tentang layanan transportasi umum. Kemacetan lalu lintas di kota-kota besar dan ketegangan publik dengan keamanan transportasi umum diselesaikan dengan adanya aplikasi transportasi online seperti Grab dan Gojek yang memberikan kemudahan dan kenyamanan bagi penggunanya Penelitian ini dilakukan untuk menganalisa keaktifan percakapan brand jasa transportasi online di jejaring sosial Twitter berdasarkan properti jaringan. Penelitian dilakukan dengan dengan mengambil data dari percakapan pengguna di social media Twitter dengan cara crawling menggunakan Bahasa pemrograman R programming dan software R Studio dan pembuatan model jaringan dengan software Gephy. Setelah itu data dianalisis menggunakan metode social network analysis yang terdiri berdasarkan properti jaringan yaitu size, density, modularity, diameter, average degree, average path length, dan clustering coefficient dan nantinya hasil analisis akan dibandingkan dari setiap properti jaringan kedua brand jasa transportasi Online dan ditentukan strategi dalam meningkatkan dan mempertahankan keaktifan serta tingkat kehadiran brand jasa transportasi online, Grab dan Gojek.

The configuration model

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Degree Sequence ◽  
Graph Model ◽  
Network Models ◽  
Clustering Coefficient ◽  
Giant Component ◽  
Configuration Model ◽  
Bipartite Networks ◽  
Small Component ◽  
Random Graph Model ◽  
Average Size

A discussion of the most fundamental of network models, the configuration model, which is a random graph model of a network with a specified degree sequence. Following a definition of the model a number of basic properties are derived, including the probability of an edge, the expected number of multiedges, the excess degree distribution, the friendship paradox, and the clustering coefficient. This is followed by derivations of some more advanced properties including the condition for the existence of a giant component, the size of the giant component, the average size of a small component, and the expected diameter. Generating function methods for network models are also introduced and used to perform some more advanced calculations, such as the calculation of the distribution of the number of second neighbors of a node and the complete distribution of sizes of small components. The chapter ends with a brief discussion of extensions of the configuration model to directed networks, bipartite networks, networks with degree correlations, networks with high clustering, and networks with community structure, among other possibilities.

Random graphs

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Random Graph ◽  
Random Graphs ◽  
Large Scale ◽  
Random Network ◽  
Graph Model ◽  
Clustering Coefficient ◽  
Giant Component ◽  
Random Graph Model ◽  
Definition Of ◽  
Average Size

An introduction to the mathematics of the Poisson random graph, the simplest model of a random network. The chapter starts with a definition of the model, followed by derivations of basic properties like the mean degree, degree distribution, and clustering coefficient. This is followed with a detailed derivation of the large-scale structural properties of random graphs, including the position of the phase transition at which a giant component appears, the size of the giant component, the average size of the small components, and the expected diameter of the network. The chapter ends with a discussion of some of the shortcomings of the random graph model.

scholarly journals Turán-type results for intersection graphs of boxes

2021 ◽  
pp. 1-6
Author(s):  
István Tomon ◽  
Dmitriy Zakharov
Keyword(s):  
Short Note ◽  
Intersection Graph ◽  
Intersection Graphs ◽  
Poset Dimension ◽  
Axis Parallel ◽  
Turán Theorem ◽  
Separation Dimension

Abstract In this short note, we prove the following analog of the Kővári–Sós–Turán theorem for intersection graphs of boxes. If G is the intersection graph of n axis-parallel boxes in $${{\mathbb{R}}^d}$$ such that G contains no copy of K t,t , then G has at most ctn( log n)2d+3 edges, where c = c(d)>0 only depends on d. Our proof is based on exploring connections between boxicity, separation dimension and poset dimension. Using this approach, we also show that a construction of Basit, Chernikov, Starchenko, Tao and Tran of K2,2-free incidence graphs of points and rectangles in the plane can be used to disprove a conjecture of Alon, Basavaraju, Chandran, Mathew and Rajendraprasad. We show that there exist graphs of separation dimension 4 having superlinear number of edges.

scholarly journals Effect of Multishell Diffusion MRI Acquisition Strategy and Parcellation Scale on Rich-Club Organization of Human Brain Structural Networks

Diagnostics ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 970
Author(s):  
Maedeh Khalilian ◽  
Kamran Kazemi ◽  
Mahshid Fouladivanda ◽  
Malek Makki ◽  
Mohammad Sadegh Helfroush ◽  
...  
Keyword(s):  
Human Brain ◽  
Clustering Coefficient ◽  
Quality Data ◽  
B Values ◽  
Rich Club ◽  
Global Efficiency ◽  
Acquisition Strategy ◽  
The Rich ◽  
Structural Networks ◽  
Single Shell

The majority of network studies of human brain structural connectivity are based on single-shell diffusion-weighted imaging (DWI) data. Recent advances in imaging hardware and software capabilities have made it possible to acquire multishell (b-values) high-quality data required for better characterization of white-matter crossing-fiber microstructures. The purpose of this study was to investigate the extent to which brain structural organization and network topology are affected by the choice of diffusion magnetic resonance imaging (MRI) acquisition strategy and parcellation scale. We performed graph-theoretical network analysis using DWI data from 35 Human Connectome Project subjects. Our study compared four single-shell (b = 1000, 3000, 5000, 10,000 s/mm2) and multishell sampling schemes and six parcellation scales (68, 200, 400, 600, 800, 1000 nodes) using five graph metrics, including small-worldness, clustering coefficient, characteristic path length, modularity and global efficiency. Rich-club analysis was also performed to explore the rich-club organization of brain structural networks. Our results showed that the parcellation scale and imaging protocol have significant effects on the network attributes, with the parcellation scale having a substantially larger effect. Regardless of the parcellation scale, the brain structural networks exhibited a rich-club organization with similar cortical distributions across the parcellation scales involving at least 400 nodes. Compared to single b-value diffusion acquisitions, the deterministic tractography using multishell diffusion imaging data consisting of shells with b-values higher than 5000 s/mm2 resulted in significantly improved fiber-tracking results at the locations where fiber bundles cross each other. Brain structural networks constructed using the multishell acquisition scheme including high b-values also exhibited significantly shorter characteristic path lengths, higher global efficiency and lower modularity. Our results showed that both parcellation scale and sampling protocol can significantly impact the rich-club organization of brain structural networks. Therefore, caution should be taken concerning the reproducibility of connectivity results with regard to the parcellation scale and sampling scheme.

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