Reliability of scale-free complex networks

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.

Impact of social neighborhood on diffusion of innovation S-curve

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.

Collective decision making is crucial in human organizations and societies. When a collective is working on exploration of problem space and/or ideation for creative solutions, the evolutionary perspective is useful for conceptualizing and modeling collective decision making, where populations of ideas spread and evolve on a social network habitat via continual applications of evolutionary operators by human individuals (Sayama & Dionne 2015). Using an evolutionary approach to model collective decision making, we conducted agent-based simulations to investigate how collective decision making would be affected by the size and topology of social network structure (Sayama, Dionne & Yammarino 2013). In our model, each agent has its own utility function defined over a multi-dimensional problem space, which is marginally different from the “true” utility function that is not accessible from any agent. Each agent can memorize multiple ideas in mind, and iteratively applies evolutionary operators (e.g., replication, mutation, recombination, elimination) to the idea population it has. The outcomes of evolutionary operations are stored in the agent’s mind, and also sent to the neighbors to which the agent is connected. This allows the spread of ideas through social ties. Each simulation was run for a fixed number of iterations, and then the level of idea convergence at a social level and the true utility value of the most supported idea were measured as the performance metrics of collective decision making. The former metric characterizes the ability for the society to form consensus, while the latter characterizes its ability to find the true best solution. The size of the network (number of agents or nodes) was varied from 5 to 640 logarithmically. Three network topologies with the same average node degree were tested: Random, small-world and scale-free. For more details of the model and the simulation settings, see Sayama, Dionne & Yammarino (2013). Simulation results indicated that expanding the size of the social network generally improved the quality of ideas at the cost of decision convergence. Simulations with different social network topologies further revealed that collective decision making on small-world networks with high local clustering tended to achieve highest decision quality more often than on random or scale-free networks (Fig. 1). This can be understood in that local clustering helps agents in different regions in a network maintain their respective focus areas and engage in different local search, possibly enhancing the effective parallelism of collective decision making and therefore resulting in a greater number of successful decisions. In contrast, the links in random and scale-free networks are all “global”, mixing discussions prematurely and therefore reducing the effective parallelism of collective decision making. These observations have an interesting contrast with the fact that random and scale-free networks are highly efficient in information dissemination because of their global connectedness. Our results indicate that such efficiency of information dissemination may not necessarily imply the same for collective decision making. This work may also offer an evolutionary explanation for the nontrivial relationship between network clustering and problem solving, a problem that is actively debated in organizational science (Shore, Bernstein & Lazer 2014).

Collective decision making is crucial in human organizations and societies. When a collective is working on exploration of problem space and/or ideation for creative solutions, the evolutionary perspective is useful for conceptualizing and modeling collective decision making, where populations of ideas spread and evolve on a social network habitat via continual applications of evolutionary operators by human individuals (Sayama & Dionne 2015). Using an evolutionary approach to model collective decision making, we conducted agent-based simulations to investigate how collective decision making would be affected by the size and topology of social network structure (Sayama, Dionne & Yammarino 2013). In our model, each agent has its own utility function defined over a multi-dimensional problem space, which is marginally different from the “true” utility function that is not accessible from any agent. Each agent can memorize multiple ideas in mind, and iteratively applies evolutionary operators (e.g., replication, mutation, recombination, elimination) to the idea population it has. The outcomes of evolutionary operations are stored in the agent’s mind, and also sent to the neighbors to which the agent is connected. This allows the spread of ideas through social ties. Each simulation was run for a fixed number of iterations, and then the level of idea convergence at a social level and the true utility value of the most supported idea were measured as the performance metrics of collective decision making. The former metric characterizes the ability for the society to form consensus, while the latter characterizes its ability to find the true best solution. The size of the network (number of agents or nodes) was varied from 5 to 640 logarithmically. Three network topologies with the same average node degree were tested: Random, small-world and scale-free. For more details of the model and the simulation settings, see Sayama, Dionne & Yammarino (2013). Simulation results indicated that expanding the size of the social network generally improved the quality of ideas at the cost of decision convergence. Simulations with different social network topologies further revealed that collective decision making on small-world networks with high local clustering tended to achieve highest decision quality more often than on random or scale-free networks (Fig. 1). This can be understood in that local clustering helps agents in different regions in a network maintain their respective focus areas and engage in different local search, possibly enhancing the effective parallelism of collective decision making and therefore resulting in a greater number of successful decisions. In contrast, the links in random and scale-free networks are all “global”, mixing discussions prematurely and therefore reducing the effective parallelism of collective decision making. These observations have an interesting contrast with the fact that random and scale-free networks are highly efficient in information dissemination because of their global connectedness. Our results indicate that such efficiency of information dissemination may not necessarily imply the same for collective decision making. This work may also offer an evolutionary explanation for the nontrivial relationship between network clustering and problem solving, a problem that is actively debated in organizational science (Shore, Bernstein & Lazer 2014).

In this paper, we present an efficient opinion control strategy for complex networks, in particular, for social networks. The proposed adaptive bridge control (ABC) strategy calls for controlling a special kind of nodes named bridge and requires no knowledge of the node degrees or any other global or local knowledge, which are necessary for some other immunization strategies including targeted immunization and acquaintance immunization. We study the efficiency of the proposed ABC strategy on random networks, small-world networks, scale-free networks, and the random networks adjusted by the edge exchanging method. Our results show that the proposed ABC strategy is efficient for all of these four kinds of networks. Through an adjusting clustering coefficient by the edge exchanging method, it is found out that the efficiency of our ABC strategy is closely related with the clustering coefficient. The main contributions of this paper can be listed as follows: (1) A new high-order social network is proposed to describe opinion dynamic. (2) An algorithm, which does not require the knowledge of the nodes' degree and other global∕local network structure information, is proposed to control the "bridges" more accurately and further control the opinion dynamics of the social networks. The efficiency of our ABC strategy is illustrated by numerical examples. (3) The numerical results indicate that our ABC strategy is more efficient for networks with higher clustering coefficient.

Fractal dimensions of percolating networks

This chapter extends an established model of Brownian agent to investigate the role of social networks in migration and economic aggregation under a multiregion system. The regional conditions are represented by three variables: wage level, tax rate, and welfare. In the model, Brownian agents make their movements by exploiting their social networks to find regional locations with better incomes. We examined the model under four types of network structures: (1) complete network, (2) random network, (3) regular network, and (4) scale-free network. Via computer simulations, the results prove that social networks affect agent migration and economic aggregation and reduce the stability of the whole system. Some findings are summarized as follows: 1. Regardless of the network structure, agents always move to locations with a high welfare service. 2. Agents move frequently when the network has highly connected links (complete and random network) and no obvious economic center appears and remains, whereas in the case of a loosely connected network (regular and scale-free network), agents mainly migrate to regions with a high tax rate for better welfare; the multiregion system finally evolves toward a stable state.

In this paper, we compare the efficiency of fault detection and diagnosis in networks having different topological properties, such as scale-free networks and Erdos-Renyi random graphs. Efficiency measures include both the number of tests (e.g., end-to-end network probes) necessary for diagnosis and the computational complexity of diagnosis. We observe that diagnosis in scale-free networks typically requires significantly larger number of tests than diagnosis in random networks. However, the computational complexity of diagnosis appears to be much lower for scale-free networks since the corresponding Bayesian network models used for probabilistic diagnosis tend to have much lower induced width - a topological parameter controlling the complexity of inference in Bayesian networks. We believe that our observations provide important insights for design and deployment of cost-efficient diagnostic methods in computer networks and distributed systems.

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 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.

Offdiagonal complexity: A computationally quick complexity measure for graphs and networks

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.

This study examined the application of network theory to skilled passing behaviour in a team sport by considering small-world and scale-free network models. Using data obtained from a 2006 soccer game in Japan between Japan and Ghana, we counted the number of passes by each player within 5-minute intervals. The structural properties of the passing behaviour, which included a characteristic path length and clustering coefficient, and the degree of distribution were analysed. This showed that the structural property of the passing behaviour represented neither a complete graph nor a random graph; rather, it reflected a small-world or scale-free network. In addition, the probabilities of outgoing and incoming passes reflected links that followed a power-law distribution. Passing behaviour in a soccer match appeared to be similar to behaviour in social networks with smaller vertices in terms of the scale-free property and a self-organising mechanism.

We study evolving networks where new nodes when attached to the network form links with other nodes of preferred distances. A particular case is where always the shortest distances are selected ("make friends with the friends of your present friends"). We present simulation results for network parameters like the first eigenvalue of the graph Laplacian (synchronizability), clustering coefficients, average distances, and degree distributions for different distance preferences and compare them with the parameter values for random and scale-free networks. We find that for the shortest distance rule we obtain a power-law degree distribution as in scale-free networks, while the other parameters are significantly different, especially the clustering coefficient.