Non-Consensus Opinion Model with Byzantine Nodes

This paper first constructs a tiered network model of the interbank market. Then, from the perspective of contagion risk, it studies numerically the resilience of four types of interbank market network models to shocks, namely, tiered networks, random networks, small‐world networks, and scale‐free networks. This paper studies the interbank market with homogeneous and heterogeneous banks and analyzes random shocks and selective shocks. The study reveals that tiered interbank market networks and random interbank market networks are basically more vulnerable against selective shocks, while small‐world interbank market networks and scale‐free interbank market networks are generally more vulnerable against random shocks. Besides, the results indicate that, in the four types of interbank market networks, scale‐free networks have the highest stability against shocks, while small‐world networks are the most vulnerable. When banks are homogeneous, faced with selective shocks, the stability of the tiered interbank market networks is slightly lower than that of random interbank market networks, whereas, in other cases, the stability of the tiered interbank market networks is basically between that of random interbank market networks and that of scale‐free interbank market networks.

It is now known that the complexity of network topology has a great impact on the stabilization of complex dynamical networks. In this work, we study the control of random networks and scale-free networks. Conditions are investigated for globally or locally stabilizing such networks. Our strategy is to apply local feedback control to a small fraction of network nodes. We propose the concept of virtual control for microscopic dynamics throughout the process with different pinning schemes for both random networks and scale-free networks. We explain the main reason why significantly less local controllers are required by specifically pinning the most highly connected nodes in a scale-free network than those required by the randomly pinning scheme, and why there is no significant difference between specifically and randomly pinning schemes for controlling random dynamical networks. We also study the synchronization phenomenon of controlled dynamical networks in the stabilization process, both analytically and numerically.

In this paper, we propose a new model for continuous time opinion dynamics on an evolving network. As opposed to existing models, in which the network typically evolves by discretely adding or removing edges, we instead propose a model for opinion formation which is coupled to a network evolving through a system of ordinary differential equations for the edge weights. We interpret each edge weight as the strength of the relationship between a pair of individuals, with edges increasing in weight if pairs continually listen to each other’s opinions and decreasing if not. We investigate the impact of various edge dynamics at different timescales on the opinion dynamics itself. This is done partly through analytic results and partly through extensive numerical simulations of two case studies: one using bounded confidence interaction dynamics in the opinion formation process (as in the classical Hegselmann–Krause model) and one using an exponentially decaying interaction function. We find that the dynamic edge weights can have a significant impact on the opinion formation process, since they may result in consensus formation but can also reinforce polarisation. Overall, the proposed modelling approach allows us to quantify and investigate how the network and opinion dynamics influence each other.

Scale-free networks, as one major class of complex networks, are characterized by a specific structural feature of power-law degree distributions. Examples of scale-free real-world networks include World Wide Web (WWW), email networks, citation and co-author scientific networks, social networks (Facebook, Twitter), networks of Internet routers, and protein-protein interaction networks. In this paper we model and evaluate the reliability of scale-free complex networks using a binary decision diagram (BDD)-based method. Two-terminal reliability is considered, which is defined as the probability that a specified pair of nodes can communication through at least one fault-tree path in the network. This reliability metric can measure, for example, how reliable the information can be shared between two parties or in general how reliable the information can be disseminated within a social network. The Barabasi-Albert model is used for generating the sample scale-free networks studied in this paper. The reliability performance of scale-free networks is compared to that of random networks under the Erdos-Renyi model. Degree distributions and clustering coefficients (average fraction of pairs of neighbors of a node which are also neighbors of each other) of sample scale-free and random networks are illustrated and compared. Their effects on the performance of the BDD-based method for the reliability analysis of both scale-free and random networks are also discussed.

Uncorrelated random scale-free (URSF) networks are useful null models for checking the effects of scale-free topology on network-based dynamical processes. Here, we present a comparative study of the jamming level of gradient networks based on URSF networks and Erdős–Rényi (ER) random networks. We find that the URSF networks are less congested than ER random networks for the average degree ⟨k⟩>kc (kc ≈ 2 denotes a critical connectivity). In addition, by investigating the topological properties of the two kinds of gradient networks, we discuss the relations between the topological structure and the transport efficiency of the gradient networks. These findings show that the uncorrelated scale-free structure might allow more efficient transport than the random structure.

In a network cliques are fully connected subgraphs that reveal which are the tight communities present in it. Cliques of size c > 3 are present in random Erdös and Renyi graphs only in the limit of diverging average connectivity.Starting from the finding that real scale-free graphs have large cliques, we study the clique number in uncorrelated scale-free networks finding both upper and lower bounds. Interestingly, we find that in scale-free networks large cliques appear also when the average degree is finite, i.e. even for networks with power law degree distribution exponents γ∊(2,3). Moreover, as long as γ < 3, scale-free networks have a maximal clique which diverges with the system size.

Page rank is a ranking algorithm based on a random surfer model which is used in Google search engine and many other domains. Because of its initial success in Google search engine, page rank has become the de-facto choice when it comes to ranking nodes in a network structure. Despite the ubiquitous utility of the algorithm, little is known about the effect of topology on the performance of the page rank algorithm. Hence this paper discusses the performance of page rank algorithm under different topological conditions. We use scale-free networks and random networks along with a custom search engine we implemented in order to experimentally prove that the performance of page rank algorithm is deteriorated when the random network is perturbed. In contrast, scale-free topology is proven to be resilient against degree preserving perturbations which aids the page rank algorithm to deliver consistent results across multiple networks that are perturbed to varying proportions. Not only does the top ranking results emerge as stable nodes, but the overall performance of the algorithm is proven to be remarkably resilient which deepens our understanding about the risks in applying page rank algorithm without an initial analysis on the underlying network structure. The results conclusively suggests that while page rank algorithm can be applied to scale-free networks with relatively low risk, applying page rank algorithm to other topologies can be risky as well as misleading. Therefore, the success of the page rank algorithm in real world in search engines such as Google is at least partly due to the fact that the world wide web is a scale-free network. Since the world wide web is constantly evolving, we postulate that if the topological structure of the world wide web changes significantly so that it loses its scale-free nature to some extent, the page rank algorithm will not be as effective.

This paper investigates the impact of network structure on latency in complex networks under two different routing strategies. The performances of both scale-free networks and random networks are compared and evaluated under the shortest path routing strategy and least cost routing strategy. Our study shows that under the shortest path routing strategy, the scale-free network fares much worse compared to the random network. Conversely, under the least cost routing, the performance of the scale-free network far exceeds that of the random network because of its unique network structure.

Purpose Building on the Lau and Murnighan’s theory of fault line strength, Flache and Mäs (2008b) proposed a computational opinion dynamics model to explore the effect of demographic fault line strength on team cohesion. This study aims to extend the Flache–Mäs (FM) model to incorporate geographical location and the dyadic communication regime in opinion formation process. More specifically, we make spatially proximate agents more likely to interact with each other in the dyadic communication regime. Our results show that when agents update their opinion after each pairwise encounter, opinion polarization is lower at steady state compared to when they update their opinion after interacting with all agents. In addition, if nearby agents are more likely to interact with each other, we see greater polarization compared to the FM model with the dyadic communication regime. An immediate policy implication of this result is that organizational managers should design work space in a way that encourage wider communications between members of a team and avoid geographically local communication. Design/methodology/approach We introduce our computational models to study the effect of location and the dyadic communication regime on team performance (as measured by agents’ opinions on various work-related issues) in the presence of a strong demographic fault line. Our models are extensions of the FM model. For clarification purposes, first we describe the FM model and then elaborate our extensions. Findings The most important finding of this paper is that the timing of interactions plays an important role in steady state of opinion space in a given population. The reason can be traced to the path-dependent nature of social systems, in which initial adopters of a certain opinion or an ideology can significantly change the final configuration of a population. For example, if an early adopter of a given work-related issue in an organization has an extremely positive view toward that issue, and s/he interacts with nearby employees who have similar demographic attributes, we would expect to find an extreme opinion cluster with respect to that issue after a while. However, depending on factors that affect the timing of interaction between individuals, we would expect different outcome in the same organization. If, for instance, more extreme people are more likely to interact, the results would be different compared to when moderate agents are more likely to interact. Originality/value One immediate policy implication of the results of this paper is that organizational managers should design work space in a way that encourage wider communications between members of a team and avoid geographically local communication, if they are to temper the negative effect of a strong demographic fault line. However, they should be cautious and take other related findings into account to avoid undesirable outcomes. For example, according to Flache and Mäss’s results, managers can also initially encourage discussion within demographically homogenous groups and avoid controversial work-related issues. In addition, previous studies showed that more contacts between agents may increase opinion polarization. Our results provide no evidence for more complex and modern organizational designs where individuals or teams do not have a fixed location or stable geographical pattern. For instance, in a modern car manufacturing shop floor, it is possible that workers have to move with cars, or operational engineers have to move between different sections and places. Furthermore, there may be a flexible and dynamic work schedule for workers such that they share a same work station but in different time, which requires a more complex model than what we presented in this paper. In this sense, the geographical setting analyzed in this paper should not be generalized to all organizations or companies. We also have no evidence about other critical factors that might affect the communication and activation regime of individuals. For example, one could imagine a case that workers with the same level of skill in a specific work-related issue are more likely to interact with each other. Moreover, some specific organizational structures could impose additional restrictions on who can/should interact with whom.

We study a system consisting of diffusively coupled noisy bistable elements on a scale-free random network. This system exhibits an order-disorder phase transition as the noise intensity is varied. The phase ordering process takes place consecutively and in order of the degrees, reflecting strong degree heterogeneity of the scale-free network. A nonlinear Fokker-Planck equation describing the network dynamics is derived under mean-field approximation of the network, and is used to explain the phase ordering dynamics of the system.

In this paper we assess the vulnerability of different synthetic complex networks by measuring the traffic performance in presence of intentional nodes and edge attacks. We choose which nodes or edges would be attacked by using several centrality measures, such as: degree, eigenvector and betweenness centrality. In order to obtain some information about the vulnerability of the four different complex networks (random, small world, scale-free and random geometric) we analyze the throughput of these networks when the nodes or the edges are attacked using some of the above mentioned strategies. When attack happens, the bandwidth is reallocated among the flows, which affects the traffic utility. One of the obtained results shows that the scale-free network gives the best flow performance and then comes random networks, small world, and the poorest performance is given by the random geometric networks. This changes dramatically after removing some of the nodes (or edges), giving the biggest performance drop to random and scale-free networks and smallest to random geometric and small world networks.

Activity at rest provides valuable information about functional organization of brain networks. However, lack of cellular resolution in human brain imaging techniques precludes analysis of some of the key properties of resting state networks. Here we used a large-scale c-Fos imaging of resting state neuronal activity in the mouse brain combined with graph analysis methods to get deeper insights into structure and functional significance of resting state brain networks. We compared experimentally identified networks with model networks having the same parameters of edges and nodes: random, scale free and small world networks, using parameters of clustering and global efficiency. Clustering of experimental networks was at the same level as in scale free network – the number of clusters in experimental networks exceeded the random level. However, global efficiency analysis revealed that these clusters have weak interactions with each other or even no interaction at all – thus the global efficiency of experimental networks was at the same level as of a random network. We also found that a single strong traumatic experience can lead to global and long-term changes in the structure of resting state networks. The resting state network of mice which underwent traumatic experience had greater entropy than that of naive mice, especially in the zone of increased influence of strong correlations. We suggest that these changes reflect replay of neuronal assemblies involved in the states of past experience.

This article investigates the Multiple Equilibria Regulation (MER) model, i.e., an agent-based simulation model, to represent opinion dynamics in social networks. It relies on a small set of micro-prerequisites (intra-individual balance and confidence bound), leading to emergence of (non)stationary macro-outcomes. These outcomes may refer to consensus, polarization or fragmentation of opinions about taxation (e.g., congestion pricing) or other policy measures, according to the way communication is structured. In contrast with other models of opinion dynamics, it allows for the impact of both the regulation of intra-personal discrepancy and the interpersonal variability of opinions on social learning and network dynamics. Several simulation experiments are presented to demonstrate, through the MER model, the role of different network structures (complete, star, cellular automata, small-world and random graphs) on opinion formation dynamics and the overall evolution of the system. The findings can help to identify specific topological characteristics, such as density, number of neighbourhoods and critical nodes-agents, that affect the stability and system dynamics. This knowledge can be used to better organize the information diffusion and learning in the community, enhance the predictability of outcomes and manage possible conflicts. It is shown that a small-world organization, which depicts more realistic aspects of real-life and virtual social systems, provides increased predictability and stability towards a less fragmented and more manageable grouping of opinions, compared to random networks. Such macro-level organizations may be enhanced with use of web-based technologies to increase the density of communication and public acceptability of policy measures.

Objective: To compare cardiovascular and ventilatory variables in upright versus aero cycle ergometry at submaximal and maximal exercise intensities in untrained cyclists. Method: Ten physically active men (mean (SD) age...

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