Diffusion/Contagion Processes on Social Networks

2020 ◽  
Vol 47 (2) ◽  
pp. 235-248 ◽  
Author(s):  
Thomas W. Valente ◽  
George G. Vega Yon
Keyword(s):  
Diffusion Of Innovations ◽  
Small World ◽  
Opinion Leadership ◽  
Random Networks ◽  
Degree Centrality ◽  
Health Educators ◽  
Normal Threshold ◽  
Scale Free ◽  
Threshold Distribution ◽  
New Ideas

This study models how new ideas, practices, or diseases spread within and between communities, the diffusion of innovations or contagion. Several factors affect diffusion such as the characteristics of the initial adopters, the seeds; the structure of the network over which diffusion occurs; and the shape of the threshold distribution, which is the proportion of prior adopting peers needed for the focal individual to adopt. In this study, seven seeding conditions are modeled: (1) three opinion leadership indicators, (2) two bridging measures, (3) marginally positioned seeds, and (4) randomly selected seeds for comparison. Three network structures are modeled: (1) random, (2) small-world, and (3) scale-free. Four threshold distributions are modeled: (1) normal; (2) uniform; (3) beta 7,14; and (4) beta 1,2; all of which have a mean threshold of 33%, with different variances. The results show that seeding with nodes high on in-degree centrality and/or inverse constraint has faster and more widespread diffusion. Random networks had faster and higher prevalence of diffusion than scale-free ones, but not different from small-world ones. Compared with the normal threshold distribution, the uniform one had faster diffusion and the beta 7,14 distribution had slower diffusion. Most significantly, the threshold distribution standard deviation was associated with rate and prevalence such that higher threshold standard deviations accelerated diffusion and increased prevalence. These results underscore factors that health educators and public health advocates should consider when developing interventions or trying to understand the potential for behavior change.

Diffusion of innovations in Axelrod’s model on small-world networks

2020 ◽  
Vol 31 (08) ◽  
pp. 2050116
Author(s):  
Sandro M. Reia
Keyword(s):  
Long Range ◽  
Diffusion Of Innovations ◽  
Computational Models ◽  
Single Agent ◽  
Finite Size ◽  
Small World ◽  
Single Feature ◽  
State Formula ◽  
New Ideas ◽  
Text Features

The interest in learning how innovations spread in our society has led to the development of a variety of theoretical-computational models to describe the mechanisms that govern the diffusion of new ideas among people. In this paper, the diffusion of innovations is addressed with the use of the Axelrod’s cultural model where an agent is represented by a cultural vector of [Formula: see text] features, in which each feature can take on [Formula: see text] integer states. The innovation or new idea is introduced in the population by setting a single feature of a single agent to a new state ([Formula: see text]) in the initial configuration. Particularly, we focus on the effect of the small-world topology on the dynamics of the innovation adoption. Our results indicate that the innovation spreads sublinearly ([Formula: see text]) in a regular one-dimensional lattice of connectivity [Formula: see text], whereas the innovation spreads linearly ([Formula: see text]) when a nonvanishing fraction of the short-ranged links are replaced by long-range ones. In addition, we find that the small-world topology prevents the emergence of complete order in the thermodynamic limit. For systems of finite size, however, the introduction of long range links causes the dynamics to reach a final ordered state much more rapidly than for the regular lattice.

scholarly journals Statistical Analysis to Bitcoin Transactions Network

2020 ◽  
Vol 9 (5) ◽  
pp. 85
Author(s):  
Argyrios Kalampakas ◽  
Georgios C. Makris
Keyword(s):  
Economic Activity ◽  
Scientific Evidence ◽  
Small World ◽  
Holistic Approach ◽  
Research Community ◽  
Statistical Analyses ◽  
Random Networks ◽  
Scale Free ◽  
Network Analyses ◽  
Financial Transactions

There is abundantly documented scientific evidence that the financial transactions that have grown rapidly recently, in conjuction with the interest of the public, were due to the sharp rise in the price of Bitcoin in December 2017. As a consequence, a freshly emerging dataset in the research community has emerged. Therefore, the aim of the present investigation was to examine the analyses of data in this newly emerging dataset in the research community. In order to achieve the extraction of data, their conversion to network and finally their fragmentation, the studied variables were analyzed by using two parts of analysis, namely, statistical network analyses and economic activity analyses. Network statistical analyses was employed aiming to analyze, in a holistic approach, the complex systems of modern times which are represented as networks, as it is impossible to analyze them partially, in order to avoid incorrect conclusions. Additionally, the analyses of economic activity, which is related to indicators from the stock market and the economics of science, was used, after it had been transferred and matched with the economic model represented by Bitcoin. The results distinguished the extent of the data generated by the statistical analyses of the networks and the analyses of economic activity. With respect to data presented, we established that the daily transaction networks were scale free networks which were not evolving like ER random networks and they were not defined as the small world. Also, it was demonstrated that daily transaction networks cannot be reproduced in a random way like ER random networks. Furthermore, the opportunities and problems encountered in conducting the present research were briefly presented.

Reduced Topologically Real-World Networks

2015 ◽  
Vol 6 (2) ◽  
pp. 13-27 ◽  
Author(s):  
Marcello Trovati
Keyword(s):  
Real World ◽  
Data Analytics ◽  
Big Data Analytics ◽  
Small World ◽  
Random Networks ◽  
Large Dataset ◽  
Ongoing Research ◽  
Scale Free ◽  
Usable Information ◽  
Complex Interactions

The topological and dynamical properties of real-world networks have attracted extensive research from a variety of multi-disciplinary fields. They, in fact, model typically big datasets which pose interesting challenges, due to their intrinsic size and complex interactions, as well as the dependencies between their different sub-parts. Therefore, defining networks based on such properties, is unlikely to produce usable information due to their complexity and the data inconsistencies which they typically contain. In this paper, the authors discuss the evaluation of a method as part of ongoing research which aims to mine data to assess whether their associated networks exhibit properties comparable to well-known structures, namely scale-free, small world and random networks. For this, they will use a large dataset containing information on the seismologic activity recorded by the European-Mediterranean Seismological Centre. The authors will show that it provides an accurate, agile, and scalable tool to extract useful information. This further motivates their effort to produce a big data analytics tool which will focus on obtaining in-depth intelligence from both structured and unstructured big datasets. This will ultimately lead to a better understanding and prediction of the properties of the system(s) they model.

Loss distribution of systemic defaults in different interbank networks

2016 ◽  
Vol 27 (10) ◽  
pp. 1650121 ◽  
Author(s):  
Shouwei Li ◽  
Jianmin He
Keyword(s):  
Network Structure ◽  
Small World ◽  
Default Probability ◽  
Random Networks ◽  
Interbank Market ◽  
Small World Networks ◽  
Loss Distribution ◽  
Loss Given Default ◽  
Scale Free ◽  
The Impact

We analyze the impact of the network structure, the default probability and the loss given default (LGD) on the loss distribution of systemic defaults in the interbank market, where network structures analyzed include random networks, small-world networks and scale-free networks. We find that the network structure has little effect on the shape of the loss distribution, whereas the opposite is true to the default probability; the LGD changes the shape of the loss distribution significantly when default probabilities are high; the maximum of the possible loss is sensitive to the network structure and the LGD.

Using Networks to Measure Influence and Impact

2014 ◽  
Vol 556-562 ◽  
pp. 2668-2671
Author(s):  
Li Xian Zhang ◽  
Yu Jia Liu ◽  
Xin Zhong Lu
Keyword(s):  
Social Network ◽  
Complex Network ◽  
Calculation Result ◽  
Betweenness Centrality ◽  
Small World ◽  
Closeness Centrality ◽  
Degree Centrality ◽  
Scale Free ◽  
Important Type ◽  
Ranking Order

The co-author networks are important type of social network. In this paper, we establishes the Erdös co-author network and proves that the Erdös co-author network is a complex network which has three main properties, including small world, scale-free and clustering properties. Besides, this article gives the calculation formulas for degree centrality, closeness centrality and betweenness centrality of a network. According to the calculation result we give a ranking order for authors within Erdös co-author network.

RISK ASSESSMENT OF ATTACK-INDUCED CASCADE IN COMPLEX NETWORKS

2011 ◽  
Vol 22 (08) ◽  
pp. 765-773
Author(s):  
ZHE-JING BAO ◽  
WEN-JUN YAN ◽  
CHUANG-XIN GUO
Keyword(s):  
Risk Assessment ◽  
Complex Networks ◽  
Quantitative Evaluation ◽  
Small World ◽  
Random Networks ◽  
Small World Network ◽  
Scale Free Network ◽  
Scale Free ◽  
Probability Of Occurrence ◽  
Free Network

For the complex networks, including scale-free, small-world, local-world and random networks, the global quantitative evaluation of attack-induced cascade is investigated in this paper by introducing the risk assessment, which integrates the probability of occurrence with the damage size of attacks on nodes. It is discovered by simulations, among the several kinds of networks, that the small-world network has the largest risk assessment of attack-induced cascade; the risk assessment of three other networks are all very low and the most protection against attack should be given to the small-world network accordingly. Furthermore, the percentage of the most fragile nodes in the scale-free network is very low, compared with that in the small-world network.

scholarly journals Network Entropy and Systemic Risk in Dynamic Banking Systems

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Liang He ◽  
Shouwei Li
Keyword(s):  
Systemic Risk ◽  
Random Network ◽  
Small World ◽  
Random Networks ◽  
Scale Free Network ◽  
Small World Networks ◽  
Scale Free ◽  
Banking Systems ◽  
Free Network ◽  
Network Entropy

We investigate network entropy of dynamic banking systems, where interbank networks analyzed include random networks, small-world networks, and scale-free networks. We find that network entropy is positively correlated with the effect of systemic risk in the three kinds of interbank networks and that network entropy in the small-world network is the largest, followed by those in the random network and the scale-free network.

Top Museums on Instagram

2019 ◽  
Vol 3 (2) ◽  
pp. 18-42 ◽  
Author(s):  
Vasiliki G. Vrana ◽  
Dimitrios A. Kydros ◽  
Evangelos C. Kehris ◽  
Anastasios-Ioannis T. Theocharidis ◽  
George I. Kavavasilis
Keyword(s):  
Social Network ◽  
Network Analysis ◽  
Small World ◽  
Marketing Strategies ◽  
The Other ◽  
Small World Network ◽  
Scale Free ◽  
Centrality Metrics ◽  
Photo Sharing ◽  
Visualization Algorithms

Pictures speak louder than words. In this fast-moving world where people hardly have time to read anything, photo-sharing sites become more and more popular. Instagram is being used by millions of people and has created a “sharing ecosystem” that also encourages curation, expression, and produces feedback. Museums are moving quickly to integrate Instagram into their marketing strategies, provide information, engage with audience and connect to other museums Instagram accounts. Taking into consideration that people may not see museum accounts in the same way that the other museum accounts do, the article first describes accounts' performance of the top, most visited museums worldwide and next investigates their interconnection. The analysis uses techniques from social network analysis, including visualization algorithms and calculations of well-established metrics. The research reveals the most important modes of the network by calculating the appropriate centrality metrics and shows that the network formed by the museum Instagram accounts is a scale–free small world network.

STABILITY OF TWO TYPICAL COMPLEX DYNAMICAL NETWORKS

2008 ◽  
Vol 22 (05) ◽  
pp. 553-560 ◽  
Author(s):  
WU-JIE YUAN ◽  
XIAO-SHU LUO ◽  
PIN-QUN JIANG ◽  
BING-HONG WANG ◽  
JIN-QING FANG
Keyword(s):  
Numerical Simulation ◽  
Dissipative System ◽  
Small World ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
General Complex ◽  
The Stability ◽  
Theoretical Results

When being constructed, complex dynamical networks can lose stability in the sense of Lyapunov (i. s. L.) due to positive feedback. Thus, there is much important worthiness in the theory and applications of complex dynamical networks to study the stability. In this paper, according to dissipative system criteria, we give the stability condition in general complex dynamical networks, especially, in NW small-world and BA scale-free networks. The results of theoretical analysis and numerical simulation show that the stability i. s. L. depends on the maximal connectivity of the network. Finally, we show a numerical example to verify our theoretical results.

Independence polynomial and matching polynomial of the Koch network

2015 ◽  
Vol 29 (32) ◽  
pp. 1550234
Author(s):  
Yunhua Liao ◽  
Xiaoliang Xie
Keyword(s):  
Lattice Gas ◽  
Small World ◽  
Partition Functions ◽  
Complete Class ◽  
Dimer Model ◽  
Scale Free ◽  
Matching Polynomial ◽  
Independence Polynomial ◽  
Classical Models ◽  
Explicit Formulae

The lattice gas model and the monomer-dimer model are two classical models in statistical mechanics. It is well known that the partition functions of these two models are associated with the independence polynomial and the matching polynomial in graph theory, respectively. Both polynomials have been shown to belong to the “[Formula: see text]-complete” class, which indicate the problems are computationally “intractable”. We consider these two polynomials of the Koch networks which are scale-free with small-world effects. Explicit recurrences are derived, and explicit formulae are presented for the number of independent sets of a certain type.

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