A Random Network Generator with Finely Tunable Clustering Coefficient for Small-World Social Networks

Recent evidence suggests that pulmonary vein isolation (PVI) may perturb the electrophysiological substrate for maintenance of atrial fibrillation (AF). Our previous work indicates that information theory metrics can quantify electrical communications during arrhythmia. We hypothesized that PVI ‘rewires’ the electrical communication network during AF such that the topology exhibits higher levels of small-world network properties, with higher clustering coefficient and lower path length, than would be expected by chance. Thirteen consecutive patients (n=6 with prior PVI and n=7 without) underwent AF ablation using a 64-electrode basket catheter in the left atrium. Multielectrode recording was performed during AF for 60 seconds, followed by PVI. Mutual information was calculated from the time series between each pair of electrodes using the Kraskov-Stögbauer-Grassberger estimator. The all-to-all mutual information matrix (64x64; Figure, upper panels) was thresholded by the median and standard deviations of mutual information to build a binary adjacency matrix for electrical communication networks. The properties of small-world network ( swn ; ‘small-world-ness’) were quantified by the ratio of the observed average clustering coefficient to that of a random network over the ratio of the observed average path length to that of a random network. swn was expressed in normal Z standard deviation units. As the binarizing threshold increased, the Z-score of swn decreased (Figure, lower panel). However, the Z-score at each threshold value was consistently higher with prior PVI than those without (p<0.05). In conclusion, electrical communication network during AF with prior PVI is associated with higher levels of small-world network properties than those without. This finding supports the concept that PVI perturbs the underlying substrate. In addition, swn of electrical communication network may be a promising metric to quantify substrate modification.

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A NEW DYNAMIC COMMUNITY MODEL FOR SOCIAL NETWORKS

International Journal of Modern Physics C ◽

10.1142/s0129183113500885 ◽

2014 ◽

Vol 25 (02) ◽

pp. 1350088 ◽

Cited By ~ 2

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.

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Networking Agglomeration Effect of E-Commerce Platform in Industry Clusters

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.631-632.1140 ◽

2014 ◽

Vol 631-632 ◽

pp. 1140-1144

Author(s):

Zong Qiang Ren ◽

Hong Bin Zhang

Keyword(s):

Social Networks ◽

Small World ◽

Clustering Coefficient ◽

Third Party ◽

Industry Clusters ◽

Agglomeration Effect ◽

Evolution Of Structure

Agglomeration effect of e-commerce platform based on industry clusters is demonstrated from locus of social networks with Ucinet 6.0. An industry zone of electrical manufacturing districts in China is investigated to describe the evolution of structure based on e-commerce platform from emergence to aggregation. The result shows that based on e-commerce platform, small world features of industry clusters are obvious with shorter distance and higher clustering coefficient, and resources flow and configuration is faster than before. E-commerce platform can diversify the nature of clustering with high heterogeneity and betweenness. However, the sharply increased network centralization would indicate control advantages for third-party of e-commerce firms, even monopoly.

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Network-based approach to explore basin network comparing observed and satellite dataset

10.5194/egusphere-egu21-4840 ◽

2021 ◽

Author(s):

Mayuri Gadhawe ◽

Ravi Kumar Guntu ◽

Ankit Agarwal

Keyword(s):

Correlation Coefficient ◽

Random Network ◽

Pearson Correlation ◽

Correlation Method ◽

Small World ◽

Clustering Coefficient ◽

Node Degree ◽

Network Measures ◽

Network Properties ◽

Precipitation Network

<p>Complex network is a relatively young, multidisciplinary field with an objective to unravel the spatiotemporal interaction in natural processes. Though network theory has become a very important paradigm in many fields, the applications in the hydrology field are still at an emerging stage.&#160; In this study, we employed the Pearson correlation coefficient and Spearman correlation coefficient as a similarity measure with varying threshold ranges to construct the precipitation network of the Ganga River Basin (GRB). Ground-based observed dataset (IMD) and satellite precipitation product (TRMM) are used. Different network properties such as node degree, degree distribution, clustering coefficient, and architecture were computed on each resultant precipitation network of GRB. We also ranked influential grid points in the precipitation network by using weighted degree betweenness to identify the importance of each grid station in the network Our results reveal that the choice of correlation method does not significantly affect the network measures and reconfirm that the thresholds significantly influence network construction and network properties in the case of both datasets. The spatial distribution of the clustering coefficient value is high to low from center to boundary and inverse in the case of degree.&#160; In addition, there is a positive correlation between the average neighbor degree and node degree. Again, we analyzed the architecture of precipitation networks and found that the network has a small world with random network behavior. &#160;&#160;Our results also indicated that both products have similar network measures and showed similar kinds of spatial patterns.</p>

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Game theoretical inference of human behavior in social networks

Nature Communications ◽

10.1038/s41467-019-13148-8 ◽

2019 ◽

Vol 10 (1) ◽

Cited By ~ 1

Author(s):

Nicolò Pagan ◽

Florian Dörfler

Keyword(s):

Social Networks ◽

Network Formation ◽

Preferential Attachment ◽

Estimation Method ◽

Small World ◽

User Preferences ◽

Clustering Coefficient ◽

Real World Data ◽

Trade Offs ◽

The Impact

AbstractSocial networks emerge as a result of actors’ linking decisions. We propose a game-theoretical model of socio-strategic network formation on directed weighted graphs, in which every actors’ benefit is a parametric trade-off between centrality measure, brokerage opportunities, clustering coefficient, and sociological network patterns. We use two different stability definitions to infer individual behavior of homogeneous, rational agents from network structure, and to quantify the impact of cooperation. Our theoretical analysis confirms results known for specific network motifs studied previously in isolation, yet enables us to precisely quantify the trade-offs in the space of user preferences. To deal with complex networks of heterogeneous and irrational actors, we construct a statistical behavior estimation method using Nash equilibrium conditions. We provide evidence that our results are consistent with empirical, historical, and sociological observations on real-world data-sets. Furthermore, our method offers sociological and strategic interpretations of random networks models, such as preferential attachment and small-world networks.

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Evolution of Conformity Dynamics in Complex Social Networks

Symmetry ◽

10.3390/sym11030299 ◽

2019 ◽

Vol 11 (3) ◽

pp. 299 ◽

Cited By ~ 2

Author(s):

Yuhui Gong ◽

Qian Yu

Keyword(s):

Social Networks ◽

Random Network ◽

Small World ◽

Network Size ◽

Small World Network ◽

Scale Free Network ◽

Small World Networks ◽

Dominant Group ◽

Scale Free ◽

Free Network

Conformity is a common phenomenon among people in social networks. In this paper, we focus on customers’ conformity behaviors in a symmetry market where customers are located in a social network. We establish a conformity model and analyze it in ring network, random network, small-world network, and scale-free network. Our simulations shown that topology structure, network size, and initial market share have significant effects on the evolution of customers’ conformity behaviors. The market will likely converge to a monopoly state in small-world networks but will form a duopoly market in scale networks. As the size of the network increases, there is a greater possibility of forming a dominant group of preferences in small-world network, and the market will converge to the monopoly of the product which has the initial selector in the market. Also, network density will become gradually significant in small-world networks.

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Reinterpretaion of the friendship paradox

International Journal of Modern Physics C ◽

10.1142/s0129183117500243 ◽

2017 ◽

Vol 28 (02) ◽

pp. 1750024

Author(s):

Jingcheng Fu ◽

Jianliang Wu

Keyword(s):

Social Networks ◽

Random Network ◽

Network Models ◽

Mean Value ◽

Clustering Coefficient ◽

Probability Method ◽

Price Model ◽

Power Law Exponent ◽

The Mean ◽

Shed Light

The friendship paradox (FP) is a sociological phenomenon stating that most people have fewer friends than their friends do. It is to say that in a social network, the number of friends that most individuals have is smaller than the average number of friends of friends. This has been verified by Feld. We call this interpreting method mean value version. But is it the best choice to portray the paradox? In this paper, we propose a probability method to reinterpret this paradox, and we illustrate that the explanation using our method is more persuasive. An individual satisfies the FP if his (her) randomly chosen friend has more friends than him (her) with probability not less than [Formula: see text]. Comparing the ratios of nodes satisfying the FP in networks, [Formula: see text], we can see that the probability version is stronger than the mean value version in real networks both online and offline. We also show some results about the effects of several parameters on [Formula: see text] in random network models. Most importantly, [Formula: see text] is a quadratic polynomial of the power law exponent [Formula: see text] in Price model, and [Formula: see text] is higher when the average clustering coefficient is between [Formula: see text] and [Formula: see text] in Petter–Beom (PB) model. The introduction of the probability method to FP can shed light on understanding the network structure in complex networks especially in social networks.

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Random graphs

10.1093/oso/9780198805090.003.0011 ◽

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.

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Sublinear domination and core–periphery networks

Scientific Reports ◽

10.1038/s41598-021-94105-8 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Marios Papachristou

Keyword(s):

Network Model ◽

Power Law ◽

Real World ◽

Random Network ◽

Small World ◽

The Core ◽

Entire Network

AbstractIn this paper we devise a generative random network model with core–periphery properties whose core nodes act as sublinear dominators, that is, if the network has n nodes, the core has size o(n) and dominates the entire network. We show that instances generated by this model exhibit power law degree distributions, and incorporates small-world phenomena. We also fit our model in a variety of real-world networks.

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Modifications in the Topological Structure of EEG Functional Connectivity Networks during Listening Tonal and Atonal Concert Music in Musicians and Non-Musicians

Brain Sciences ◽

10.3390/brainsci11020159 ◽

2021 ◽

Vol 11 (2) ◽

pp. 159

Author(s):

Almudena González ◽

Manuel Santapau ◽

Antoni Gamundí ◽

Ernesto Pereda ◽

Julián J. González

Keyword(s):

Topological Structure ◽

Phase Synchronization ◽

Random Network ◽

Small World ◽

Surrogate Data ◽

Musical Structure ◽

Beta Band ◽

Tonal Music ◽

Frequency Bands ◽

Concert Music

The present work aims to demonstrate the hypothesis that atonal music modifies the topological structure of electroencephalographic (EEG) connectivity networks in relation to tonal music. To this, EEG monopolar records were taken in musicians and non-musicians while listening to tonal, atonal, and pink noise sound excerpts. EEG functional connectivities (FC) among channels assessed by a phase synchronization index previously thresholded using surrogate data test were computed. Sound effects, on the topological structure of graph-based networks assembled with the EEG-FCs at different frequency-bands, were analyzed throughout graph metric and network-based statistic (NBS). Local and global efficiency normalized (vs. random-network) measurements (NLE|NGE) assessing network information exchanges were able to discriminate both music styles irrespective of groups and frequency-bands. During tonal audition, NLE and NGE values in the beta-band network get close to that of a small-world network, while during atonal and even more during noise its structure moved away from small-world. These effects were attributed to the different timbre characteristics (sounds spectral centroid and entropy) and different musical structure. Results from networks topographic maps for strength and NLE of the nodes, and for FC subnets obtained from the NBS, allowed discriminating the musical styles and verifying the different strength, NLE, and FC of musicians compared to non-musicians.

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