scholarly journals Snowdrift Game on Topologically Alterable Complex Networks

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Zhe Wang ◽  
Hong Yao ◽  
Jun Du ◽  
Xingzhao Peng ◽  
Chao Ding
Keyword(s):  
Complex Networks ◽  
Power Law ◽  
Network Models ◽  
Average Degree ◽  
Clustering Coefficient ◽  
Topological Parameters ◽  
Snowdrift Game ◽  
Cooperation Level ◽  
Optimal Value ◽  
Power Law Exponent

In order to study the influence of network’s structure on cooperation level of repeated snowdrift game, in the frame of two kinds of topologically alterable network models, the relation between the cooperation density and the topological parameters was researched. The results show that the network’s cooperation density is correlated reciprocally with power-law exponent and positively with average clustering coefficient; in other words, the more homogenous and less clustered a network, the lower the network’s cooperation level; and the relation between average degree and cooperation density is nonmonotonic; when the average degree deviates from the optimal value, the cooperation density drops.

scholarly journals The diameter of KPKVB random graphs

2019 ◽  
Vol 51 (2) ◽  
pp. 358-377 ◽  
Author(s):  
Tobias Müller ◽  
Merlijn Staps
Keyword(s):  
Complex Networks ◽  
Power Law ◽  
Degree Sequence ◽  
Graph Model ◽  
Clustering Coefficient ◽  
Maximum Diameter ◽  
Hyperbolic Distance ◽  
Random Graph Model ◽  
Power Law Exponent ◽  
Law Degree

AbstractWe consider a random graph model that was recently proposed as a model for complex networks by Krioukov et al. (2010). In this model, nodes are chosen randomly inside a disk in the hyperbolic plane and two nodes are connected if they are at most a certain hyperbolic distance from each other. It has previously been shown that this model has various properties associated with complex networks, including a power-law degree distribution and a strictly positive clustering coefficient. The model is specified using three parameters: the number of nodes N, which we think of as going to infinity, and $\alpha, \nu > 0$, which we think of as constant. Roughly speaking, $\alpha$ controls the power-law exponent of the degree sequence and $\nu$ the average degree. Earlier work of Kiwi and Mitsche (2015) has shown that, when $\alpha \lt 1$ (which corresponds to the exponent of the power law degree sequence being $\lt 3$), the diameter of the largest component is asymptotically almost surely (a.a.s.) at most polylogarithmic in N. Friedrich and Krohmer (2015) showed it was a.a.s. $\Omega(\log N)$ and improved the exponent of the polynomial in $\log N$ in the upper bound. Here we show the maximum diameter over all components is a.a.s. $O(\log N),$ thus giving a bound that is tight up to a multiplicative constant.

Joint Combat System of Systems Modeling and Effectiveness Analysis Based on Complex Networks

2012 ◽  
Vol 591-593 ◽  
pp. 1589-1592 ◽  
Author(s):  
Yan Bo Qi ◽  
Liu Zhong ◽  
Le Zhang ◽  
Jiang Hu Xu
Keyword(s):  
Complex Networks ◽  
Network Models ◽  
System Of Systems ◽  
Clustering Coefficient ◽  
Network Effect ◽  
Scale Free ◽  
Effectiveness Analysis ◽  
Joint Operations ◽  
The Difference ◽  
Basic Network

How to describe the difference among various combat networks and measure their effectiveness is an important problem in combat analysis. In this paper three basic network models are developed based on the theory of complex networks and a new method is put forward for measuring the network effect of combat SoS. Numerical comparisons of the three combat network models indicate that though integrated joint operations network has the highest networked effects in networked effectiveness and clustering coefficient, but when considering the Average Path Length index, it has the lowest effectiveness. The results also suggest that the degree distribution of integrated joint operations network is scale-free thus it has the highest survivability.

STRUCTURAL CHANGES CAUSED BY ERROR AND ATTACK TOLERANCE IN US AIRPORT NETWORK

2004 ◽  
Vol 18 (17n19) ◽  
pp. 2394-2400 ◽  
Author(s):  
L. P. CHI ◽  
X. CAI
Keyword(s):  
Power Law ◽  
Weight Distribution ◽  
Degree Distribution ◽  
Structural Changes ◽  
Average Degree ◽  
Clustering Coefficient ◽  
Error Tolerance ◽  
Topological Properties ◽  
Original Network ◽  
High Degree

Through the study of US airport network, we find that the network displays a high degree of error tolerance and an extreme vulnerability to attacks. The topological properties, including average degree, clustering coefficient, diameter and efficiency, are slightly affected when a few least connected airports are removed. Such properties change drastically with the removal of a few most connected ones. The degree distribution and the weight distribution under errors behave similarly to those of the original network. Under attacks, the degree distribution changes from a two-segment power-law to a monotonic one. While the under-attacked weight distribution still displays a power-law tail, with the exponent changing from 1.50 to 1.24.

SNAM

2016 ◽  
pp. 215-236 ◽  
Author(s):  
Bassant Youssef ◽  
Scott F. Midkiff ◽  
Mohamed R. M. Rizk
Keyword(s):  
Community Structure ◽  
Complex Networks ◽  
Degree Distribution ◽  
Network Models ◽  
Small World ◽  
Clustering Coefficient ◽  
Network Nodes ◽  
Scale Free ◽  
Complex Network Models ◽  
Novel Model

Complex networks are characterized by having a scale-free power-law (PL) degree distribution, a small world phenomenon, a high average clustering coefficient, and the emergence of community structure. Most proposed models did not incorporate all of these statistical properties and neglected incorporating the heterogeneous nature of network nodes. Even proposed heterogeneous complex network models were not generalized for different complex networks. We define a novel aspect of node-heterogeneity which is the node connection standard heterogeneity. We introduce our novel model “settling node adaptive model” SNAM which reflects this new nodes' heterogeneous aspect. SNAM was successful in preserving PL degree distribution, small world phenomenon and high clustering coefficient of complex networks. A modified version of SNAM shows the emergence of community structure. We prove using mathematical analysis that networks generated using SNAM have a PL degree distribution.

scholarly journals Geometrical congruence and efficient greedy navigability of complex networks

2020 ◽  
Author(s):  
Carlo Cannistraci ◽  
Alessandro Muscoloni
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Hyperbolic Space ◽  
Power Law ◽  
Shortest Paths ◽  
Network Measure ◽  
Power Law Exponent ◽  
Current Belief ◽  
Networks Analysis ◽  
Structural Brain

Abstract Hyperbolic networks are supposed to be congruent with their underlying latent geometry and following geodesics in the hyperbolic space is believed equivalent to navigate through topological shortest paths (TSP). This assumption of geometrical congruence is considered the reason for nearly maximally efficient greedy navigation of hyperbolic networks. Here, we propose a complex network measure termed geometrical congruence (GC) and we show that there might exist different TSP, whose projections (pTSP) in the hyperbolic space largely diverge, and significantly differ from the respective geodesics. We discover that, contrary to current belief, hyperbolic networks do not demonstrate in general geometrical congruence and efficient navigability which, in networks generated with nPSO model, seem to emerge only for power-law exponent close to 2. We conclude by showing that GC measure can impact also real networks analysis, indeed it significantly changes in structural brain connectomes grouped by gender or age.

Reinterpretaion of the friendship paradox

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.

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.

scholarly journals Modelling community structure and temporal spreading on complex networks

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Vesa Kuikka
Keyword(s):  
Community Structure ◽  
Complex Networks ◽  
Community Detection ◽  
Network Structure ◽  
Network Connectivity ◽  
Network Models ◽  
Building Blocks ◽  
Detection Algorithm ◽  
Research Area ◽  
Detection Methods

AbstractWe present methods for analysing hierarchical and overlapping community structure and spreading phenomena on complex networks. Different models can be developed for describing static connectivity or dynamical processes on a network topology. In this study, classical network connectivity and influence spreading models are used as examples for network models. Analysis of results is based on a probability matrix describing interactions between all pairs of nodes in the network. One popular research area has been detecting communities and their structure in complex networks. The community detection method of this study is based on optimising a quality function calculated from the probability matrix. The same method is proposed for detecting underlying groups of nodes that are building blocks of different sub-communities in the network structure. We present different quantitative measures for comparing and ranking solutions of the community detection algorithm. These measures describe properties of sub-communities: strength of a community, probability of formation and robustness of composition. The main contribution of this study is proposing a common methodology for analysing network structure and dynamics on complex networks. We illustrate the community detection methods with two small network topologies. In the case of network spreading models, time development of spreading in the network can be studied. Two different temporal spreading distributions demonstrate the methods with three real-world social networks of different sizes. The Poisson distribution describes a random response time and the e-mail forwarding distribution describes a process of receiving and forwarding messages.

scholarly journals Analysis of Air Mean Temperature Anomalies by Using Horizontal Visibility Graphs

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 207
Author(s):  
Javier Gómez-Gómez ◽  
Rafael Carmona-Cabezas ◽  
Elena Sánchez-López ◽  
Eduardo Gutiérrez de Ravé ◽  
Francisco José Jiménez-Hornero
Keyword(s):  
Complex Networks ◽  
Global Climate ◽  
Spatial Relation ◽  
Clustering Coefficient ◽  
Horizontal Visibility ◽  
Climate Conditions ◽  
Mean Values ◽  
Intrinsic Nature ◽  
Temperature Anomalies ◽  
Mean Temperature

The last decades have been successively warmer at the Earth’s surface. An increasing interest in climate variability is appearing, and many research works have investigated the main effects on different climate variables. Some of them apply complex networks approaches to explore the spatial relation between distinct grid points or stations. In this work, the authors investigate whether topological properties change over several years. To this aim, we explore the application of the horizontal visibility graph (HVG) approach which maps a time series into a complex network. Data used in this study include a 60-year period of daily mean temperature anomalies in several stations over the Iberian Peninsula (Spain). Average degree, degree distribution exponent, and global clustering coefficient were analyzed. Interestingly, results show that they agree on a lack of significant trends, unlike annual mean values of anomalies, which present a characteristic upward trend. The main conclusions obtained are that complex networks structures and nonlinear features, such as weak correlations, appear not to be affected by rising temperatures derived from global climate conditions. Furthermore, different locations present a similar behavior and the intrinsic nature of these signals seems to be well described by network parameters.

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