Homogeneous Small-world Networks Research Articles

Local acceptance and emergence of consensus in a heterogeneous small-world network of agents with and without memory

We formulate a spatiotemporal model of social interaction that explores the role of local acceptance or influence in consensus-building. It is applied to a population of interacting agents that forms a small-world Watts–Strogatz network to determine the level of consensus that emerges as a function of the local acceptance parameter α(0≤α≤1), agent memory capacity, and interaction scale. Parameter α sets the probability that an agent copies the majority state of its neighbors while (1−α) is the corresponding likelihood that it conforms with the minority state. An agent with memory may retain its present state regardless of the local state of its neighborhood. We track the emergence of global agreement in a heterogeneous population of agents with and without memory, using density metrics that correspond to three different interaction scales — entire population, neighborhoods, and pairs of agents. We have found that for a given α and population heterogeneity, the degree of agreement would depend strongly on the chosen interaction scale and network connectivity. Unlike its disordered counterpart, a homogeneous small-world network with memory, is unable to reach a simple majority of 51% over a wide range of α < 0.83. The degree of agreement then peaks towards 80% at α=0.95 before decreasing rapidly back to 50% as α→1.0. Memory prevents a heterogeneous small-world network from achieving full agreement at α=1.0, even when the agents with memory is a weak minority. All density profiles are asymmetric about α=0.5, indicating the uneven impact of copying the majority or minority state in consensus building. They are also distinct and difficult to extrapolate from each other. The model provides an adaptive platform for exploring the spatiotemporal performance of existing collective decision-making strategies either separately or in multiple combination of each other. It can be deployed to probe the possible triggers of strategy modification in adaptive social networks. We have identified its presence in animal groups that were observed while in pursuit of predefined tasks such as group emergency evacuation.

Self-questioning dynamical evolutionary game in small-world networks

Self-questioning update rules is the selected process of the optimal strategy of the individuals by comparing the payoff from various alternative strategies. In this paper, a self-questioning dynamical evolutionary game with altruistic or spiteful preferences via weighted sums of own and opponents payoffs is studied. In order to obtain the influence of long-range connections and degree heterogeneity on evolutionary game model, we study three kinds of spatial structure: the two-dimensional lattice, homogeneous small-world networks (only the introduction of long-range connections) and heterogenous small-world networks (both long-range connections and degree heterogeneity). Through the Ising model theory and Monte Carlo simulation the following conclusions are obtained: long-range connections make the individuals perplex in strategic choice which is similar to the state of frustration in spin glass; the degree heterogeneity makes the different individual has the different field (the more neighbours, the larger of field); when the field is positive, long-range connections promote cooperation, but the heterogeneity of degree inhibits the production of cooperation.

A multi-community homogeneous small-world network and its fundamental characteristics

Abstract We introduce a new small-world network–which we call the multi-community homogeneous-small-world network–that is divided into multiple communities that are relatively isolated, similar to sparsely connected islands. A generating algorithm is presented and its network parameters are explored. To elucidate the fundamental characteristics of the proposed topology, we adopt spatial prisoner’s dilemma games as a template for discussion. Comparing with a conventional homogeneous small-world network, more enhanced network reciprocity is observed in games where a stag hunt-type dilemma is large. With intensive analysis, we find how this enhancement is brought about.

Epidemics on small worlds of tree-based wireless sensor networks

Due to link additions, small world phenomena exist in tree-based wireless sensor networks. Epidemics on small worlds of tree-based networks are studied, and the epidemic threshold at which the outbreak of the epidemic occurs is calculated. Epidemiological processes are analyzed when the infection probability is larger than the percolation threshold. Although different epidemiological processes occur on the underlying tree topology, the number of infected nodes increases exponentially as the infection spreads. The uniform immunization procedure is conducted in the homogeneous small-world network. The infection still extends exponentially although the immunization effectively reduces the prevalence speed.

Role of Clustering Coefficient on Cooperation Dynamics in Homogeneous Networks

Based on previous works, we give further investigations on the Prisoners' Dilemma Game (PDG) on two different types of homogeneous networks, i.e. the homogeneous small-world network (HSWN) and the regular ring graph. We find that the so-called resonance-like character can occur on both the networks. Different from the viewpoint in previous publications, we think the small-world effect may be unnecessary to produce this character. Therefore, over these two types of networks, we suggest a common understanding in the viewpoint of clustering coefficient. Detailed simulation results can sustain our viewpoint quite well. Furthermore, we investigate the Snowdrift Game (SG) on the same networks. The difference between the outputs of the PDG and the SG can also sustain our viewpoint.

Epidemic spreading and cooperation dynamics on homogeneous small-world networks

We introduce a class of small-world networks--homogeneous small-worlds--which, in contrast with the well-known Watts-Strogatz small-worlds, exhibit a homogeneous connectivity distribution, in the sense that all nodes have the same number of connections. This feature allows the investigation of pure small-world effects, detached from any associated heterogeneity. Furthermore, we use at profit the remarkable similarity between the properties of homogeneous small worlds and the heterogeneous small-worlds of Watts-Strogatz to assess the separate roles of heterogeneity and small-world effects. We investigate the dependence on these two mechanisms of the threshold for epidemic outbreaks and also of the coevolution of cooperators and defectors under natural selection. With respect to the well-studied regular homogeneous limits, we find a subtle interplay between these mechanisms. While they both contribute to reduce the threshold for an epidemic outburst, they exhibit opposite behavior in the evolution of cooperation, such that the overall results mask the true nature of their individual contribution to this process.