How to Quantify 'Small-World Networks'?

Fractals ◽  
1998 ◽  
Vol 06 (04) ◽  
pp. 301-303 ◽  
Author(s):  
Hanspeter Herzel
Keyword(s):  
Small World ◽  
Small World Network ◽  
Small Worlds ◽  
Small World Networks ◽  
Complete Regularity ◽  
Local Clustering ◽  
Regular Network ◽  
Analytical Expressions ◽  
Global Connection

Recently Watts and Strogatz emphasized the widespread relevance of 'small worlds' and studied numerically networks between complete regularity and complete randomness. In this letter, I derive simple analytical expressions which can reproduce the empirical observations. It is shown how a few random connections can turn a regular network into a 'small-world network' with a short global connection but persisting local clustering.

scholarly journals An evolutionary inspection game with labour unions on small-world networks

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
Salahuddin M. Kamal ◽  
Yas Al-Hadeethi ◽  
Fouad A. Abolaban ◽  
Fahad M. Al-Marzouki ◽  
Matjaž Perc
Keyword(s):  
Bargaining Power ◽  
Evolutionary Process ◽  
Small World ◽  
Small World Network ◽  
Small World Networks ◽  
Labour Unions ◽  
Long Run ◽  
Inspection Game ◽  
Overall Performance

Abstract We study an evolutionary inspection game where agents can chose between working and shirking. The evolutionary process is staged on a small-world network, through which agents compare their incomes and, based on the outcome, decide which strategy to adopt. Moreover, we introduce union members that have certain privileges, of which the extent depends on the bargaining power of the union. We determine how the union affects the overall performance of the firm that employs the agents and what are its influences on the employees. We find that, depending on its bargaining power, the union has significant leverage to deteriorate the productivity of a firm and consequently also to lower the long-run benefits of the employees.

scholarly journals Revisiting the Small-World Phenomenon

2016 ◽  
Vol 20 (1) ◽  
pp. 149-173 ◽  
Author(s):  
Tore Opsahl ◽  
Antoine Vernet ◽  
Tufool Alnuaimi ◽  
Gerard George
Keyword(s):  
Significant Variation ◽  
Random Network ◽  
Small World ◽  
Random Networks ◽  
Significant Heterogeneity ◽  
Small World Network ◽  
Small World Networks ◽  
Firm Outcomes ◽  
Baseline Levels

Research has explored how embeddedness in small-world networks influences individual and firm outcomes. We show that there remains significant heterogeneity among networks classified as small-world networks. We develop measures of the efficiency of a network, which allow us to refine predictions associated with small-world networks. A network is classified as a small-world network if it exhibits a distance between nodes that is comparable to the distance found in random networks of similar sizes—with ties randomly allocated among nodes—in addition to containing dense clusters. To assess how efficient a network is, there are two questions worth asking: (a) What is a compelling random network for baseline levels of distance and clustering? and (b) How proximal should an observed value be to the baseline to be deemed comparable? Our framework tests properties of networks, using simulation, to further classify small-world networks according to their efficiency. Our results suggest that small-world networks exhibit significant variation in efficiency. We explore implications for the field of management and organization.

MICROSCOPIC SELF-ORGANIZATION IN NETWORKS AND REGULAR LATTICE

2002 ◽  
Vol 16 (25) ◽  
pp. 923-935
Author(s):  
QI OUYANG ◽  
KAI SUN ◽  
HONGLI WANG
Keyword(s):  
Correlation Length ◽  
Random Network ◽  
Reaction System ◽  
Small World ◽  
Self Organization ◽  
Fast Diffusion ◽  
Small World Network ◽  
Regular Lattice ◽  
Numerical Studies ◽  
Regular Network

We report our numerical studies on the microscopic self-organizations of a reaction system in three types of networks: a regular network, a small-world network, and a random network as well as on a regular lattice. Our simulation results show that the topology of the network has an important effect on the communication among reaction molecules, and plays an important role in microscopic self-organization. The correlation length among reacting molecules in a random or a small-world network is much shorter compared with that in the regular network. As a result, it is much easier to obtain a microscopic self-organization in a small-world or a random network. A phase transition from a stochastic state to a synchronized state was observed when the randomness of a small-world network was increased. We also demonstrate that good synchronization activities of enzymatic turnover cycles can be developed on a regular lattice when the correlation length created by the fast diffusion of regulatory particles is large enough.

URBAN TRAFFIC CONGESTION SPREADING IN SMALL WORLD NETWORKS

2005 ◽  
Vol 19 (28) ◽  
pp. 4239-4246 ◽  
Author(s):  
HUIJUN SUN ◽  
JIANJUN WU
Keyword(s):  
Infection Rate ◽  
Traffic Congestion ◽  
Small World ◽  
Urban Traffic ◽  
Small World Network ◽  
Small World Networks ◽  
Seir Model

In this paper, two definitions about traffic congestion are proposed. We describe the traffic congestion spreading with the SEIR model of a complex small-world network. In addition, the relationships among the congestion factor, the number of average infection, the average recover rate and the infection rate are given by simulations in general traffic congestion conditions.

CONTAGION AND THE SPEED OF ADJUSTMENT IN SMALL WORLDS

2007 ◽  
Vol 09 (04) ◽  
pp. 689-704 ◽  
Author(s):  
EDWARD J. CARTWRIGHT
Keyword(s):  
Dynamic Process ◽  
Random Network ◽  
Small World ◽  
Coordination Game ◽  
Small Worlds ◽  
Small World Networks ◽  
Regular Lattice ◽  
Speed Of Adjustment ◽  
Equilibrium Shift

We model a simple dynamic process in which myopic agents are matched amongst each other to play a coordination game. The network of player interaction is varied between a regular lattice and a random network allowing us to model contagion in small world networks. Weighting times for an equilibrium shift from the risk dominated to risk dominant equilibrium are shown to be smallest in small world networks.

scholarly journals MULTIFRACTAL MEASURES ON SMALL-WORLD NETWORKS

Fractals ◽  
2006 ◽  
Vol 14 (02) ◽  
pp. 119-123 ◽  
Author(s):  
K. H. CHANG ◽  
B. C. CHOI ◽  
SEONG-MIN YOON ◽  
KYUNGSIK KIM
Keyword(s):  
First Passage Time ◽  
Small World ◽  
Passage Time ◽  
Small World Network ◽  
Small World Networks ◽  
First Passage ◽  
One Dimensional ◽  
Random Walker ◽  
Regular Networks ◽  
First Time

We investigate the multifractals of the first passage time on a one-dimensional small-world network with reflecting and absorbing barriers. The multifractals can be obtained from the distribution of the first passage time at which the random walker arrives for the first time at an absorbing barrier after starting from an arbitrary initial site. Our simulation is found to estimate the fractal dimension D0 = 0.920 ~ 0.930 for the different network sizes and random rewiring fractions. In particular, the multifractal structure breaks down into a small-world network, when the rewiring fraction p is larger than the critical value pc = 0.3. Our simulation results are compared with the numerical computations for regular networks.

scholarly journals Distributing Information in Small-World Networks: Four Social Cases of the Process of Contagion in Spain

2021 ◽  
pp. 2150008
Author(s):  
Simone Belli ◽  
Leonardo Reyes
Keyword(s):  
Small World ◽  
Social Institutions ◽  
Small World Network ◽  
Small World Networks ◽  
Stochastic Version ◽  
The Social ◽  
Affective Processes ◽  
Average Activity ◽  
Three State Model

This case study is part of a research project based in Spain between 2011 and 2014 on the social institutions and affective processes involved in what is normally referred to as social movement. Our purpose is to study how information circulates in small-world networks in which the dynamics are modeled with a stochastic version of Greenberg–Hasting’s excitable model. This is a three-state model in which a node can be in an excited, passive, or susceptible state. Only in the susceptible state does a node interact with its neighbors in the small-world network, and its interaction depends on the probability of contagion. We introduce an infection probability, which is the only parameter in our implementation of Greenberg–Hasting’s model. The small-world network is characterized by a mean connectivity parameter and by a disorder parameter. The resulting dynamics are characterized by the average activity in the network. We have found transitions from inactive to active collective regimes, and we can induce this transition by varying. We search for different dynamics within small-world networks of citizens’ organizations by going through the following steps: identifying alliance patterns; looking for robust small-world attributes and how they are constructed; and interpreting the three modes of our model.

scholarly journals PARALLELISM AND COMPLEXITY OF A SMALL-WORLD NETWORK MODEL

2016 ◽  
pp. 72-83 ◽  
Author(s):  
Robert E. Hiromoto
Keyword(s):  
Distributed Simulation ◽  
Small World ◽  
Network Simulator ◽  
Small World Network ◽  
Small World Networks ◽  
Computationally Efficient ◽  
Physical Constraints ◽  
Resource Limitations ◽  
Network Connection ◽  
Degree Of Separation

The small-world phenomena exhibits highly localized clustering and short-cut paths between vertices in a graph that reflect observed properties in social networks, epidemiological models and other real-world networks. The small-world models rely on the application of constraint-based randomness or the derivation of constraints on randomness to simulate the desired network complexities and their associated network connection properties. In this paper, rather than exploring the random properties of small-world networks, we employ deterministic strategies in the design of a computationally efficient distributed neuronal-axon network simulator that results in a small world network. These strategies are derived by addressing the parallel complexities of the proposed neuronal-axon network simulator, and also from physical constraints imposed by resource limitations of the distributed simulation architecture. The outcome of this study is the realization of a neuronal-axon network simulator that exhibits small-world characteristics of clustering with a logarithmic degree of separation between nodes without the need for long-range communication edges. The importance of this result is the deterministic application of reasoned optimization rules from which the small-world network emerges.

scholarly journals Efficient routeing in Poisson small-world networks

2006 ◽  
Vol 43 (3) ◽  
pp. 678-686 ◽  
Author(s):  
M. Draief ◽  
A. Ganesh
Keyword(s):  
Point Process ◽  
Network Model ◽  
Poisson Point Process ◽  
Continuum Model ◽  
Small World ◽  
Small World Network ◽  
Small World Networks ◽  
Dimensional Lattice ◽  
Fixed Radius

In a recent paper, Kleinberg (2000) considered a small-world network model consisting of a d-dimensional lattice augmented with shortcuts. The probability of a shortcut being present between two points decays as a power, r-α, of the distance, r, between them. Kleinberg showed that greedy routeing is efficient if α = d and that there is no efficient decentralised routeing algorithm if α ≠ d. The results were extended to a continuum model by Franceschetti and Meester (2003). In our work, we extend the result to more realistic models constructed from a Poisson point process wherein each point is connected to all its neighbours within some fixed radius, and possesses random shortcuts to more distant nodes as described above.

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