Small-world property promotes the evolution of distributive altruism

2016 ◽  
Author(s):  
Fuki Ueno ◽  
Takaya Arita
Keyword(s):  
Small World ◽  
Small World Property

scholarly journals Can recurrence networks show small-world property?

2016 ◽  
Vol 380 (35) ◽  
pp. 2718-2723 ◽  
Author(s):  
Rinku Jacob ◽  
K.P. Harikrishnan ◽  
R. Misra ◽  
G. Ambika
Keyword(s):  
Small World ◽  
Small World Property

scholarly journals Models And Mining Of On-Line Social Networks

2021 ◽  
Author(s):  
Yanhua Tian
Keyword(s):  
Social Networks ◽  
Power Law ◽  
Degree Distribution ◽  
Small World ◽  
Spectral Expansion ◽  
On Line ◽  
Simulation Results ◽  
Small World Property ◽  
P Type ◽  
Law Degree

Power law degree distribution, the small world property, and bad spectral expansion are three of the most important properties of On-line Social Networks (OSNs). We sampled YouTube and Wikipedia to investigate OSNs. Our simulation and computational results support the conclusion that OSNs follow a power law degree distribution, have the small world property, and bad spectral expansion. We calculated the diameters and spectral gaps of OSNs samples, and compared these to graphs generated by the GEO-P model. Our simulation results support the Logarithmic Dimension Hypothesis, which conjectures that the dimension of OSNs is m = [log N]. We introduced six GEO-P type models. We ran simulations of these GEO-P-type models, and compared the simulated graphs with real OSN data. Our simulation results suggest that, except for the GEO-P (GnpDeg) model, all our models generate graphs with power law degree distributions, the small world property, and bad spectral expansion.

scholarly journals Directed random geometric graphs

2019 ◽  
Vol 7 (5) ◽  
pp. 792-816
Author(s):  
Jesse Michel ◽  
Sushruth Reddy ◽  
Rikhav Shah ◽  
Sandeep Silwal ◽  
Ramis Movassagh
Keyword(s):  
Real World ◽  
Word Association ◽  
Graph Model ◽  
Small World ◽  
Geometric Graph ◽  
Clustering Coefficient ◽  
Random Geometric Graph ◽  
Random Geometric Graphs ◽  
Scale Free ◽  
Small World Property

Abstract Many real-world networks are intrinsically directed. Such networks include activation of genes, hyperlinks on the internet and the network of followers on Twitter among many others. The challenge, however, is to create a network model that has many of the properties of real-world networks such as power-law degree distributions and the small-world property. To meet these challenges, we introduce the Directed Random Geometric Graph (DRGG) model, which is an extension of the random geometric graph model. We prove that it is scale-free with respect to the indegree distribution, has binomial outdegree distribution, has a high clustering coefficient, has few edges and is likely small-world. These are some of the main features of aforementioned real-world networks. We also empirically observed that word association networks have many of the theoretical properties of the DRGG model.

scholarly journals Inferring long-distance connectivity shaped by air-mass movement for improved experimental design in aerobiology

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Maria Choufany ◽  
Davide Martinetti ◽  
Samuel Soubeyrand ◽  
Cindy E. Morris
Keyword(s):  
Large Scale ◽  
Mass Movement ◽  
Geographical Area ◽  
Small World ◽  
Long Distance ◽  
Air Mass ◽  
Key Factor ◽  
Large Geographical Area ◽  
Spatio Temporal ◽  
Small World Property

AbstractThe collection and analysis of air samples for the study of microbial airborne communities or the detection of airborne pathogens is one of the few insights that we can grasp of a continuously moving flux of microorganisms from their sources to their sinks through the atmosphere. For large-scale studies, a comprehensive sampling of the atmosphere is beyond the scopes of any reasonable experimental setting, making the choice of the sampling locations and dates a key factor for the representativeness of the collected data. In this work we present a new method for revealing the main patterns of air-mass connectivity over a large geographical area using the formalism of spatio-temporal networks, that are particularly suitable for representing complex patterns of connection. We use the coastline of the Mediterranean basin as an example. We reveal a temporal pattern of connectivity over the study area with regions that act as strong sources or strong receptors according to the season of the year. The comparison of the two seasonal networks has also allowed us to propose a new methodology for comparing spatial weighted networks that is inspired from the small-world property of non-spatial networks.

scholarly journals Specialization Models of Network Growth

2018 ◽  
Vol 7 (3) ◽  
pp. 375-392 ◽  
Author(s):  
L A Bunimovich ◽  
D C Smith ◽  
B Z Webb
Keyword(s):  
Power Law ◽  
Network Topology ◽  
Real World ◽  
Degree Distribution ◽  
Small World ◽  
Hierarchical Network ◽  
Network Growth ◽  
Complex Tasks ◽  
Small World Property ◽  
Law Degree

AbstractOne of the most important features observed in real networks is that, as a network’s topology evolves so does the network’s ability to perform various complex tasks. To explain this, it has also been observed that as a network grows certain subnetworks begin to specialize the function(s) they perform. Herein, we introduce a class of models of network growth based on this notion of specialization and show that as a network is specialized using this method its topology becomes increasingly sparse, modular and hierarchical, each of which are important properties observed in real networks. This procedure is also highly flexible in that a network can be specialized over any subset of its elements. This flexibility allows those studying specific networks the ability to search for mechanisms that describe their growth. For example, we find that by randomly selecting these elements a network’s topology acquires some of the most well-known properties of real networks including the small-world property, disassortativity and a right-skewed degree distribution. Beyond this, we show how this model can be used to generate networks with real-world like clustering coefficients and power-law degree distributions, respectively. As far as the authors know, this is the first such class of models that can create an increasingly modular and hierarchical network topology with these properties.

scholarly journals Complex network description of the ionosphere

2018 ◽  
Vol 25 (1) ◽  
pp. 233-240
Author(s):  
Shikun Lu ◽  
Hao Zhang ◽  
Xihai Li ◽  
Yihong Li ◽  
Chao Niu ◽  
...  
Keyword(s):  
Complex Network ◽  
Hypothesis Test ◽  
Small World ◽  
Dynamic Processes ◽  
Electron Content ◽  
Vertical Total Electron Content ◽  
Total Electron ◽  
Scale Free ◽  
Probabilistic Graph ◽  
Small World Property

Abstract. Complex networks have emerged as an essential approach of geoscience to generate novel insights into the nature of geophysical systems. To investigate the dynamic processes in the ionosphere, a directed complex network is constructed, based on a probabilistic graph of the vertical total electron content (VTEC) from 2012. The results of the power-law hypothesis test show that both the out-degree and in-degree distribution of the ionospheric network are not scale-free. Thus, the distribution of the interactions in the ionosphere is homogenous. None of the geospatial positions play an eminently important role in the propagation of the dynamic ionospheric processes. The spatial analysis of the ionospheric network shows that the interconnections principally exist between adjacent geographical locations, indicating that the propagation of the dynamic processes primarily depends on the geospatial distance in the ionosphere. Moreover, the joint distribution of the edge distances with respect to longitude and latitude directions shows that the dynamic processes travel further along the longitude than along the latitude in the ionosphere. The analysis of “small-world-ness” indicates that the ionospheric network possesses the small-world property, which can make the ionosphere stable and efficient in the propagation of dynamic processes.

scholarly journals Graph Concatenations to Derive Weighted Fractal Networks

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Zhanqi Zhang ◽  
Yingqing Xiao
Keyword(s):  
Geodesic Distance ◽  
Weighted Graph ◽  
Small World ◽  
System Size ◽  
Strength Distribution ◽  
Weighted Graphs ◽  
Scaling Factors ◽  
Fractal Sets ◽  
Small World Property ◽  
Similarity Dimension

Given an initial weighted graph G0, an integer m>1, and m scaling factors f1,…,fm∈0,1, we define a sequence of weighted graphs Gkk=0∞ iteratively. Provided that Gk−1 is given for k≥1, we let Gk−11,…,Gk−1m be m copies of Gk−1, whose weighted edges have been scaled by f1,…,fm, respectively. Then, Gk is constructed by concatenating G0 with all the m copies. The proposed framework shares several properties with fractal sets, and the similarity dimension dfract has a great impact on the topology of the graphs Gk (e.g., node strength distribution). Moreover, the average geodesic distance of Gk increases logarithmically with the system size; thus, this framework also generates the small-world property.

A NEW DYNAMIC COMMUNITY MODEL FOR SOCIAL NETWORKS

2014 ◽  
Vol 25 (02) ◽  
pp. 1350088 ◽  
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.

THE SMALL-WORLD PROPERTY IN NETWORKS GROWING BY ACTIVE EDGES

2011 ◽  
Vol 14 (06) ◽  
pp. 853-869 ◽  
Author(s):  
PHILIPPE J. GIABBANELLI
Keyword(s):  
Growth Mechanism ◽  
Average Distance ◽  
Network Models ◽  
Small World ◽  
Clustering Coefficient ◽  
Small World Networks ◽  
Fractal Approach ◽  
Small World Property ◽  
Complex Network Models ◽  
Similar Growth

In the last three years, we have witnessed an increasing number of complex network models based on a 'fractal' approach, in which parts of the network are repeatedly replaced by a given pattern. Our focus is on models that can be defined by repeatedly adding a pattern network to selected edges, called active edges. We prove that when a pattern network has at least two active edges, then the resulting network has an average distance at most logarithmic in the number of nodes. This suggests that real-world networks based on a similar growth mechanism are likely to have small average distance. We provide an estimate of the clustering coefficient and verify its accuracy using simulations. Using numerous examples of simple patterns, our simulations show various ways to generate small-world networks. Finally, we discuss extensions to our framework encompassing probabilistic patterns and active subnetworks.

Improved community model for social networks based on social mobility

2015 ◽  
Vol 26 (02) ◽  
pp. 1550012
Author(s):  
Zhe-Ming Lu ◽  
Zhen Wu ◽  
Hao Luo ◽  
Hao-Xian Wang
Keyword(s):  
Social Networks ◽  
Social Mobility ◽  
Turnover Rate ◽  
Small World ◽  
Community Size ◽  
Community Model ◽  
Proposed Model ◽  
Small World Property ◽  
The Relationship ◽  
Group Distribution

This paper proposes an improved community model for social networks based on social mobility. The relationship between the group distribution and the community size is investigated in terms of communication rate and turnover rate. The degree distributions, clustering coefficients, average distances and diameters of networks are analyzed. Experimental results demonstrate that the proposed model possesses the small-world property and can reproduce social networks effectively and efficiently.

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