On the influence of topological characteristics on robustness of complex networks

In this paper, we explore the relationship between the topological characteristics of a complex network and its robustness to sustained targeted attacks. Using synthesised scale-free, small-world and random networks, we look at a number of network measures, including assortativity, modularity, average path length, clustering coefficient, rich club profiles and scale-free exponent (where applicable) of a network, and how each of these influence the robustness of a network under targeted attacks. We use an established robustness coefficient to measure topological robustness, and consider sustained targeted attacks by order of node degree. With respect to scale-free networks, we show that assortativity, modularity and average path length have a positive correlation with network robustness, whereas clustering coefficient has a negative correlation. We did not find any correlation between scale-free exponent and robustness, or rich-club profiles and robustness. The robustness of small-world networks on the other hand, show substantial positive correlations with assortativity, modularity, clustering coefficient and average path length. In comparison, the robustness of Erdos-Renyi random networks did not have any significant correlation with any of the network properties considered. A significant observation is that high clustering decreases topological robustness in scale-free networks, yet it increases topological robustness in small-world networks. Our results highlight the importance of topological characteristics in influencing network robustness, and illustrate design strategies network designers can use to increase the robustness of scale-free and small-world networks under sustained targeted attacks

Evolutionary stable strategies in networked games: the influence of topology

Evolutionary game theory is used to model the evolution of competing strategies in a population of players. Evolutionary stability of a strategy is a dynamic equilibrium, in which any competing mutated strategy would be wiped out from a population. If a strategy is weak evolutionarily stable, the competing strategy may manage to survive within the network. Understanding the network-related factors that affect the evolutionary stability of a strategy would be critical in making accurate predictions about the behaviour of a strategy in a real-world strategic decision making environment. In this work, we evaluate the effect of network topology on the evolutionary stability of a strategy. We focus on two well-known strategies known as the Zero-determinant strategy and the Pavlov strategy. Zero-determinant strategies have been shown to be evolutionarily unstable in a well-mixed population of players. We identify that the Zero-determinant strategy may survive, and may even dominate in a population of players connected through a non-homogeneous network. We introduce the concept of `topological stability' to denote this phenomenon. We argue that not only the network topology, but also the evolutionary process applied and the initial distribution of strategies are critical in determining the evolutionary stability of strategies. Further, we observe that topological stability could affect other well-known strategies as well, such as the general cooperator strategy and the cooperator strategy. Our observations suggest that the variation of evolutionary stability due to topological stability of strategies may be more prevalent in the social context of strategic evolution, in comparison to the biological context

Impact of network assortativity on epidemic and vaccination behaviour

The resurgence of measles is largely attributed to the decline in vaccine adoption and the increase in mobility. Although the vaccine for measles is readily available and highly successful, its current adoption is not adequate to prevent epidemics. Vaccine adoption is directly affected by individual vaccination decisions, and has a complex interplay with the spatial spread of disease shaped by an underlying mobility (travelling) network. In this paper, we model the travelling connectivity as a scale-free network, and investigate dependencies between the network's assortativity and the resultant epidemic and vaccination dynamics. In doing so we extend an SIR-network model with game-theoretic components, capturing the imitation dynamics under a voluntary vaccination scheme. Our results show a correlation between the epidemic dynamics and the network's assortativity, highlighting that networks with high assortativity tend to suppress epidemics under certain conditions. In highly assortative networks, the suppression is sustained producing an early convergence to equilibrium. In highly disassortative networks, however, the suppression effect diminishes over time due to scattering of non-vaccinating nodes, and frequent switching between the predominantly vaccinating and non-vaccinating phases of the dynamics.Comment: 17 pages, 13 figure

The impact of study load on the dynamics of longitudinal email communications among students

With the advent of information technology, emails have gained wide acceptability among students as an asynchronous communication tool. According to the current pedagogy literature the overall trend of the use of email communication by university students has been increasing significantly since its inception, despite the rapid growth of the popularity and acceptability of other social mediums (e.g. Mobile phone and Facebook). In this study, we explore a longitudinal email communication network, which evolved under an increasing study load among 38 students throughout a university semester, using measures of social network analysis (SNA) and exponential random graph (ERG) models. This longitudinal network was divided into three waves, where each wave represents the portion of the complete longitudinal network that evolves between two consecutive observations. An increased study load was imposed through the assessment components of the course. SNA measures of degree centrality (i.e. the activity of an actor or actor popularity), betweenness centrality (i.e. the capacity to control the flow of information in a network), closeness centrality (i.e. reachable to other nodes) and reciprocity (i.e. tendency to make reciprocal links) are considered to explore this longitudinal network. ERG models are probabilistic models that are presented by locally determined explanatory variables and can effectively identify structural properties of networks. From the analysis of this email communication network, we notice that students’ network positions and behaviours change with the changes in their study load. In particular, we find that (i) students make an increased number of email communications with the in-crease of study load; (ii) the email communication network become sparse with the increase of study load; and (iii) the 2-star parameter (a subset of three nodes in which one node is connected to each of the other two nodes) and the triangle parameter (a subset of three nodes in which each node is connected to the other two nodes) can effectively explain the formation of network in wave3; whereas, the 3-star parameter (a subset of four nodes in which one node is connected to each of other three nodes) can effectively explain the formation of network in wave1 and wave2. Interpretations of these findings for the monitoring of student behaviour in online learning environments, as well as the implications for the design of assessment and the use of asynchronous tools are discussed in this paper

Disassortative Mixing and Systemic Rational Behaviour: How System Rationality Is Influenced by Topology and Placement in Networked Systems

Interdependent decisionmaking of individuals in social systems can be modelled by games played on complex networks. Players in such systems have bounded rationality, which influences the computation of equilibrium solutions. It has been shown that the ‘system rationality’, which indicates the overall rationality of a network of players, may play a key role in the emergence of scale-free or core-periphery topologies in real-world networks. In this work, we identify optimal topologies and mixing patterns of players which can maximise system rationality. Based on simulation results, we show that irrespective of the placement of nodes with higher rationality, it is the disassortative mixing of node rationality that helps to maximize system rationality in a population. In other words, the findings of this work indicate that the overall rationality of a population may improve when more players with non-similar individual rationality levels interact with each other. We identify particular topologies such as the core-periphery topology, which facilitates the optimisation of system rationality. The findings presented in this work may have useful interpretations and applications in socio-economic systems for maximizing the utility of interactions in a population of strategic players