scholarly journals Network Reconstruction in Terms of the Priori Structure Information

2021 ◽  
Vol 9 ◽  
Author(s):  
Jia-Qi Fu ◽  
Qiang Guo ◽  
Kai Yang ◽  
Jian-Guo Liu
Keyword(s):  
Small World ◽  
Random Networks ◽  
Success Rates ◽  
Small World Networks ◽  
Reconstruction Accuracy ◽  
Structure Information ◽  
Reconstruction Performance ◽  
Empirical Networks ◽  
Regular Networks ◽  
Synthetic Networks

In this paper, we investigate the reconstruction of networks based on priori structure information by the Element Elimination Method (EEM). We firstly generate four types of synthetic networks as small-world networks, random networks, regular networks and Apollonian networks. Then, we randomly delete a fraction of links in the original networks. Finally, we employ EEM, the resource allocation (RA) and the structural perturbation method (SPM) to reconstruct four types of synthetic networks with 90% priori structure information. The experimental results show that, comparing with RA and SPM, EEM has higher indices of reconstruction accuracy on four types of synthetic networks. We also compare the reconstruction performance of EEM with RA and SPM on four empirical networks. Higher reconstruction accuracy, measured by local indices of success rates, could be achieved by EEM, which are improved by 64.11 and 47.81%, respectively.

scholarly journals Evolution of Equity Norms in Small-World Networks

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
José I. Santos ◽  
David J. Poza ◽  
José M. Galán ◽  
Adolfo López-Paredes
Keyword(s):  
Regular Ring ◽  
Finite Population ◽  
Evolutionary Game ◽  
Small World ◽  
Nash Bargaining ◽  
Random Networks ◽  
Small World Networks ◽  
Nash Bargaining Game ◽  
Regular Networks ◽  
Topology Of Interactions

The topology of interactions has been proved very influential in the results of models based on learning and evolutionary game theory. This paper is aimed at investigating the effect of structures ranging from regular ring lattices to random networks, including small-world networks, in a model focused on property distribution norms. The model considers a fixed and finite population of agents who play the Nash bargaining game repeatedly. Our results show that regular networks promote the emergence of the equity norm, while less-structured networks make possible the appearance of fractious regimes. Additionally, our analysis reveals that the speed of adoption can also be affected by the network structure.

SYNCHRONIZATION IN THE FAMILY OF CHAOTIC SMALL-WORLD NETWORKS

2008 ◽  
Vol 19 (01) ◽  
pp. 111-123 ◽  
Author(s):  
LIANGMING HE ◽  
DUANWEN SHI
Keyword(s):  
Chaotic System ◽  
Average Distance ◽  
Small World ◽  
Clustering Coefficient ◽  
Small World Networks ◽  
Characteristic Path Length ◽  
Unified Chaotic System ◽  
The Family ◽  
Regular Networks ◽  
High Degree

In this paper we investigate by computer simulation the synchronizability of the family of small-world networks, which consists of identical chaotic units, such as the Lorenz chaotic system, the Chen chaotic system, Lü chaotic system, and the unified chaotic system (unit). It is shown that for weak coupling, synchronization clusters emerge in the networks whose disorder probabilities p are large but do not emerge in the networks whose disorder probabilities p are small; while for strong coupling under which the regular networks do not exhibit synchronization, all dynamical nodes, behaving as in the random networks, mutually synchronize in the networks which own very small disorder probability p and have both high degree of clustering and small average distance. Based on the concepts of clustering coefficient C(p), characteristic path length L(p) and global efficiency E(G), these phenomena are discussed briefly.

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.

Complex networks

2018 ◽  
Author(s):  
Graziano Vernizzi ◽  
Henri Orland
Keyword(s):  
Complex Networks ◽  
Small World ◽  
Laplacian Matrix ◽  
Square Lattice ◽  
Small World Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
Free Network ◽  
Scale Free Graphs ◽  
Regular Networks

This article deals with complex networks, and in particular small world and scale free networks. Various networks exhibit the small world phenomenon, including social networks and gene expression networks. The local ordering property of small world networks is typically associated with regular networks such as a 2D square lattice. The small world phenomenon can be observed in most scale free networks, but few small world networks are scale free. The article first provides a brief background on small world networks and two models of scale free graphs before describing the replica method and how it can be applied to calculate the spectral densities of the adjacency matrix and Laplacian matrix of a scale free network. It then shows how the effective medium approximation can be used to treat networks with finite mean degree and concludes with a discussion of the local properties of random matrices associated with complex networks.

scholarly journals Asymptotic Behaviour of Gossip Processes and Small-World Networks

2013 ◽  
Vol 45 (4) ◽  
pp. 981-1010 ◽  
Author(s):  
A. D. Barbour ◽  
G. Reinert
Keyword(s):  
Long Range ◽  
Branching Process ◽  
Small World ◽  
Random Variable ◽  
Random Networks ◽  
Small World Networks ◽  
Transmission Of Information ◽  
Characteristic Behaviour ◽  
Typical Distances ◽  
Common Behaviour

Both small-world models of random networks with occasional long-range connections and gossip processes with occasional long-range transmission of information have similar characteristic behaviour. The long-range elements appreciably reduce the effective distances, measured in space or in time, between pairs of typical points. In this paper we show that their common behaviour can be interpreted as a product of the locally branching nature of the models. In particular, it is shown that both typical distances between points and the proportion of space that can be reached within a given distance or time can be approximated by formulae involving the limit random variable of the branching process.

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 Asymptotic Behaviour of Gossip Processes and Small-World Networks

2013 ◽  
Vol 45 (04) ◽  
pp. 981-1010 ◽  
Author(s):  
A. D. Barbour ◽  
G. Reinert
Keyword(s):  
Long Range ◽  
Branching Process ◽  
Small World ◽  
Random Variable ◽  
Random Networks ◽  
Small World Networks ◽  
Transmission Of Information ◽  
Characteristic Behaviour ◽  
Typical Distances ◽  
Common Behaviour

Both small-world models of random networks with occasional long-range connections and gossip processes with occasional long-range transmission of information have similar characteristic behaviour. The long-range elements appreciably reduce the effective distances, measured in space or in time, between pairs of typical points. In this paper we show that their common behaviour can be interpreted as a product of the locally branching nature of the models. In particular, it is shown that both typical distances between points and the proportion of space that can be reached within a given distance or time can be approximated by formulae involving the limit random variable of the branching process.

RELEVANT CYCLES IN CHEMICAL REACTION NETWORKS

2001 ◽  
Vol 04 (02n03) ◽  
pp. 207-226 ◽  
Author(s):  
PETRA M. GLEISS ◽  
PETER F. STADLER ◽  
ANDREAS WAGNER ◽  
DAVID A. FELL
Keyword(s):  
Metabolic Network ◽  
Chemical Reaction ◽  
Small World ◽  
Chemical Reaction Networks ◽  
Reaction Networks ◽  
Random Networks ◽  
Small World Networks ◽  
External Perturbations ◽  
Transition Times ◽  
Law Degree

We characterize the distributions of short cycles in a large metabolic network previously shown to have small world characteristics and a power law degree distribution. Compared with three classes of random networks, including Erdős–Rényi random graphs and synthetic small world networks of the same connectivity, both the metabolic network and models for the chemical reaction networks of planetary atmospheres have a particularly large number of triangles and a deficit in large cycles. Short cycles reduce the length of detours when a connection is clipped, so we propose that long cycles in metabolism may have been selected against in order to shorten transition times and reduce the likelihood of oscillations in response to external perturbations.

MULTIFRACTALS ON SMALL-WORLD NETWORKS

2007 ◽  
Vol 21 (23n24) ◽  
pp. 4059-4063
Author(s):  
KYUNGSIK KIM ◽  
K. H. CHANG ◽  
DEOCK-HO HA
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. We analyze numerically 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, our simulation results are compared with the numerical computations for regular networks.

scholarly journals Breaking Apart Contact Networks with Vaccination

2020 ◽  
Author(s):  
Gianrocco Lazzari ◽  
Marcel Salathé
Keyword(s):  
Disease Outbreaks ◽  
Small World ◽  
Contact Network ◽  
Random Networks ◽  
Constant Number ◽  
Small World Networks ◽  
Transmission Potential ◽  
Social Mixing ◽  
Node Removal ◽  
The Continuum

ABSTRACTInfectious diseases can cause large disease outbreaks due to their transmission potential from one individual to the next. Vaccination is an effective way of cutting off possible chains of transmission, thereby mitigating the outbreak potential of a disease in a population. From a contact network perspective, vaccination effectively removes nodes from the network, thereby breaking apart the contact network into a much smaller network of susceptible individuals on which the disease can spread. Here, we look at the continuum of small world networks to random networks, and find that vaccination breaks apart networks in ways that can dramatically influence the maximum outbreak size. In particular, after the removal of a constant number of nodes (representing vaccination coverage), the more clustered small world networks more readily fall apart into many disjoint and small susceptible sub-networks, thus preventing large outbreaks, while more random networks remain largely connected even after node removal through vaccination. We further develop a model of social mixing that moves small world networks closer to the random regime, thereby facilitating larger disease outbreaks after vaccination. Our results show that even when vaccination is entirely random, social mixing can lead to contact network structures that strongly influence outbreak sizes. We find the largest effects to be in the regime of relatively high vaccination coverages of around 80%, where despite vaccination being random, outbreak sizes can vary by a factor of 20.

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