Measuring the dimension of partially embedded networks

Scaling phenomena have been intensively studied during the past decade in the context of complex networks. As part of these works, recently novel methods have appeared to measure the dimension of abstract and spatially embedded networks. In this paper we propose a new dimension measurement method for networks, which does not require global knowledge on the embedding of the nodes, instead it exploits link-wise information (link lengths, link delays or other physical quantities). Our method can be regarded as a generalization of the spectral dimension, that grasps the network’s large-scale structure through local observations made by a random walker while traversing the links. We apply the presented method to synthetic and real-world networks, including road maps, the Internet infrastructure and the Gowalla geosocial network. We analyze the theoretically and empirically designated case when the length distribution of the links has the form P(ρ)∼1/ρ$P\left(\rho \right)\sim 1/\rho$. We show that while previous dimension concepts are not applicable in this case, the new dimension measure still exhibits scaling with two distinct scaling regimes. Our observations suggest that the link length distribution is not sufficient in itself to entirely control the dimensionality of complex networks, and we show that the proposed measure provides information that complements other known measures.     

Research on spatial economic structure for different economic sectors from a perspective of a complex network

The economy system is a complex system, and the complex network is a powerful tool to study its complexity. Here we calculate the economic distance matrices based on annual GDP of nine economic sectors from 1995–2010 in 31 Chinese provinces and autonomous regions,¹ then build several spatial economic networks through the threshold method and the Minimal Spanning Tree method. After the analysis on the structure of the networks and the influence of geographic distance, some conclusions are drawn. First, connectivity distribution of a spatial economic network does not follow the power law. Second, according to the network structure, nine economic sectors could be divided into two groups, and there is significant discrepancy of network structure between these two groups. Moreover, the influence of the geographic distance plays an important role on the structure of a spatial economic network, network parameters are changed with the influence of the geographic distance. At last, 2000 km is the critical value for geographic distance: for real estate and finance, the spearman’s rho with l<2000$l<2000$ is bigger than that with l>2000$l>2000$, and the case is opposite for other economic sectors.     

Time-varying human mobility patterns with metapopulation epidemic dynamics

In this paper, explicitly considering the influences of an epidemic outbreak on human travel, a time-varying human mobility pattern is introduced to model the time variation of global human travel. The impacts of the pattern on epidemic dynamics in heterogeneous metapopulation networks, wherein each node represents a subpopulation with any number of individuals, are investigated by using a mean-field approach. The results show that the pattern does not alter the epidemic threshold, but can slightly lower the final average density of infected individuals as a whole. More importantly, we also find that the pattern produces different impacts on nodes with different degree, and that there exists a critical degree _kc$k_c$. For nodes with degree smaller than _kc$k_c$, the pattern produces a positive impact on epidemic mitigation; conversely, for nodes with degree larger than _kc$k_c$, the pattern produces a negative impact on epidemic mitigation.     

A model for the spread of rumors in Barrat–Barthelemy–Vespignani (BBV) networks

Rumor propagation is a typical form of social communication and plays a significant role in social life. In this paper, we studied the process of rumor propagation by accounting for the mechanism of forgetting in Barrat–Barthelemy–Vespignani (BBV) networks. First, we derived mean-field equations for rumor propagation based on the strength of the nodes in the propagation network. We then analyzed the stability of the model to determine whether a propagation threshold existed in the BBV networks. We also conducted numerical simulations of the BBV networks and found that rumors propagate more slowly in BBV networks than in unweighted networks. The numerical simulation results also demonstrated that as the forgetting rate increases, the rumor’s influence decreases in both BBV networks and unweighted networks. Finally, the simulation results confirmed that a threshold exists for rumor propagation in BBV networks, but that it was independent of the value of the stifling rate.     

Delay-induced synchronization transitions in small-world neuronal networks with hybrid electrical and chemical synapses

We study the dependence of synchronization transitions in small-world networks of bursting neurons with hybrid electrical–chemical synapses on the information transmission delay, the probability of electrical synapses, and the rewiring probability. It is shown that, irrespective of the probability of electrical synapses, the information transmission delay can always induce synchronization transitions in small-world neuronal networks, i.e., regions of synchronization and nonsynchronization appear intermittently as the delay increases. In particular, all these transitions to burst synchronization occur approximately at integer multiples of the bursting period of individual neurons. In addition, for larger probability of electrical synapses, the intermittent synchronization transition is more profound, due to the stronger synchronization ability of electrical synapses compared with chemical ones. More importantly, chemical and electrical synapses can perform complementary roles in the synchronization of hybrid small-world neuronal networks: the larger the electrical synapse strength is, the smaller the chemical synapse strength needed to achieve burst synchronization. Furthermore, the small-world topology has a significant effect on the synchronization transition in hybrid neuronal networks. It is found that increasing the rewiring probability can always enhance the synchronization of neuronal activity. The results obtained are instructive for understanding the synchronous behavior of neural systems.     

Non-equilibrium stochastic model for stock exchange market

We study the effect of the topology of industrial relationship (IR) between the companies in a stock exchange market on the universal features in the market. For this we propose a stochastic model for stock exchange markets based on the behavior of technical traders. From the numerical simulations we measure the return distribution, P(R)$P\left(R\right)$, and the autocorrelation function of the volatility, C(T)$C\left(T\right)$, and find that the observed universal features in real financial markets are originated from the heterogeneity of IR network topology. Moreover, the heterogeneous IR topology can also explain Zipf–Pareto’s law for the distribution of market value of equity in the real stock exchange markets.     

Birds of Moderately Different Feathers: Bandwagon Dynamics and the Threshold Heterogeneity of Network Neighbors

We present a simple combinatorial model of group decision‐making in a dichotomous choice situation. The independent variables in the model are group size and mean judgmental competence of group members. The dependent variables are the probabilities that the majority judgment of the group will be correct and that the best member of the group will be more likely to be correct than the group majority.

Two applications of this model are given: one a determination of isocompetence curves of groups of differing sizes and mean competence levels, the other an explication of the potential mechanisms accounting for Parkinson's only partly tongue‐in‐cheek observation that the point of ineffectiveness in a group seems to be reached when its total membership exceeds 20 or 21.     

The Evolution of Fairness in the Ultimatum Game

The article presents a model on the evolution of strategies in the Ultimatum game. In particular, the model considers the effect of role turnover and interaction structure. Past experimental studies showed that subjects behave more fairly than would be predicted by classical game theory. The goal of this model is to illuminate how fairness emerges in evolution when role turnover and preferential association are in effect. Simulation shows that evolution towards strategies of fairness is plausible. Some empirical implications are also discussed.     

Coordination in Dynamic Social Networks Under Heterogeneity

People often make choices or form opinions depending on the social relations they have, but they also choose their relations depending on their preferred behavior and their opinions. Most of the existing models of coevolution of networks and individual behavior assume that actors are homogeneous. In this article, we relax this assumption in a context in which actors try to coordinate their behavior with their partners. We investigate with a game-theoretic model whether social cohesion and coordination change when interests of actors are not perfectly aligned as compared to the homogeneous case. Using analytical and simulation methods we characterize the set of stable networks and examine the consequences of heterogeneity for social optimality and segregation in emerging networks.