Abstract:
Community structure exists in many real-world networks and has been reported being related to several functional properties of the networks. The conventional approach was partitioning nodes into communities, while some recent studies start partitioning links instead of nodes to find overlapping communities of nodes efficiently. We extended the map equation method, which was originally developed for node communities, to find link communities in networks. This method is tested on various kinds of networks and compared with the metadata of the networks, and the results show that our method can identify the overlapping role of nodes effectively. The advantage of this method is that the node community scheme and link community scheme can be compared quantitatively by measuring the unknown information left in the networks besides the community structure. It can be used to decide quantitatively whether or not the link community scheme should be used instead of the node community scheme. Furthermore, this method can be easily extended to the directed and weighted networks since it is based on the random walk.

Abstract:
We study a competition dynamics, based on the minority game, endowed with various substrate network structures. We observe the effects of the network topologies by investigating the volatility of the system and the structure of follower networks. The topology of substrate structures significantly influences the system efficiency represented by the volatility and such substrate networks are shown to amplify the herding effect and cause inefficiency in most cases. The follower networks emerging from the leadership structure show a power-law incoming degree distribution. This study shows the emergence of scale-free structures of leadership in the minority game and the effects of the interaction among players on the networked version of the game.

Abstract:
We introduce a self-organized surface growth model in 2+1 dimensions with anisotropic avalanche process, which is expected to be in the universality class of the anisotropic quenched Kardar-Parisi-Zhang equation with alternative signs of the nonlinear KPZ terms. It turns out that the surface height correlation functions in each direction scales distinctively. The anisotropic behavior is attributed to the asymmetric behavior of the quenched KPZ equation in 1+1 dimensions with respect to the sign of the nonlinear KPZ term.

Abstract:
Uncoordinated individuals in human society pursuing their personally optimal strategies do not always achieve the social optimum, the most beneficial state to the society as a whole. Instead, strategies form Nash equilibria which are often socially suboptimal. Society, therefore, has to pay a price of anarchy for the lack of coordination among its members. Here we assess this price of anarchy by analyzing the travel times in road networks of several major cities. Our simulation shows that uncoordinated drivers possibly waste a considerable amount of their travel time. Counterintuitively,simply blocking certain streets can partially improve the traffic conditions. We analyze various complex networks and discuss the possibility of similar paradoxes in physics.

Abstract:
In complex scale-free networks, ranking the individual nodes based upon their importance has useful applications, such as the identification of hubs for epidemic control, or bottlenecks for controlling traffic congestion. However, in most real situations, only limited sub-structures of entire networks are available, and therefore the reliability of the order relationships in sampled networks requires investigation. With a set of randomly sampled nodes from the underlying original networks, we rank individual nodes by three centrality measures: degree, betweenness, and closeness. The higher-ranking nodes from the sampled networks provide a relatively better characterisation of their ranks in the original networks than the lower-ranking nodes. A closeness-based order relationship is more reliable than any other quantity, due to the global nature of the closeness measure. In addition, we show that if access to hubs is limited during the sampling process, an increase in the sampling fraction can in fact decrease the sampling accuracy. Finally, an estimation method for assessing sampling accuracy is suggested.

Abstract:
Airplane boarding process is an example where disorder properties of the system are relevant to the emergence of universality classes. Based on a simple model, we present a systematic analysis of finite-size effects in boarding time, and propose a comprehensive view of the role of sequential disorder in the scaling behavior of boarding time against the plane size. Using numerical simulations and mathematical arguments, we find how the scaling behavior depends on the number of seat columns and the range of sequential disorder. Our results show that new scaling exponents can arise as disorder is localized to varying extents.

Abstract:
We investigate the totally asymmetric simple exclusion process on closed and directed random regular networks, which is a simple model of active transport in the one-dimensional segments coupled by junctions. By a pair mean-field theory and detailed numerical analyses, it is found that the correlations at junctions induce two notable deviations from the simple mean-field theory which neglects these correlations: (1) the narrower range of particle density for phase coexistence and (2) the algebraic decay of density profile with exponent $1/2$ even outside the maximal-current phase. We show that these anomalies are attributable to the effective slow bonds formed by the network junctions.

Abstract:
We study evolutionary processes induced by spatio-temporal dynamics in prebiotic evolution. Using numerical simulations we demonstrate that hypercycles emerge from complex interaction structures in multispecies systems. In this work we also find that `hypercycle hybrid' protects the hypercycle from its environment during the growth process. There is little selective advantage for one hypercycle to maintain coexistence with others. This brings the possibility of the outcompetition between hypercycles resulting in the negative effect on information diversity. To enrich the information in hypercycles, symbiosis with parasites is suggested. It is shown that symbiosis with parasites can play an important role in the prebiotic immunology.

Abstract:
We study zero-temperature Glauber dynamics for Ising-like spin variable models in quenched random networks with random zero-magnetization initial conditions. In particular, we focus on the absorbing states of finite systems. While it has quite often been observed that Glauber dynamics lets the system be stuck into an absorbing state distinct from its ground state in the thermodynamic limit, very little is known about the likelihood of each absorbing state. In order to explore the variety of absorbing states, we investigate the probability distribution profile of the active link density after saturation as the system size $N$ and $$ vary. As a result, we find that the distribution of absorbing states can be split into two self-averaging peaks whose positions are determined by $$, one slightly above the ground state and the other farther away. Moreover, we suggest that the latter peak accounts for a non-vanishing portion of samples when $N$ goes to infinity while $$ stays fixed. Finally, we discuss the possible implications of our results on opinion dynamics models.

Abstract:
We study the structure of the load-based spanning tree (LST) that carries the maximum weight of the Erdos-Renyi (ER) random network. The weight of an edge is given by the edge-betweenness centrality, the effective number of shortest paths through the edge. We find that the LSTs present very inhomogeneous structures in contrast to the homogeneous structures of the original networks. Moreover, it turns out that the structure of the LST changes dramatically as the edge density of an ER network increases, from scale free with a cutoff, scale free, to a starlike topology. These would not be possible if the weights are randomly distributed, which implies that topology of the shortest path is correlated in spite of the homogeneous topology of the random network.