[en] This study aims at figuring out the crucial topological ingredients which affect the outcomes of the ultimatum game located on different networks, encompassing the regular network, the random network, the small-world network, and the scale-free network. With the aid of random interchanging algorithm, we investigate the relations between the outcomes of the ultimatum game and some topological ingredients, including the average range, the clustering coefficient and the heterogeneity, and so forth. It is found that for the regular, random and small-work networks, the average range and the clustering coefficient have evident impacts on the ultimatum game, while for the scale-free network, the original degree heterogeneity and the underlying rich-club characterizations are the mainly important topological ingredients that influence the outcomes of ultimatum game substantially.

[en] Weak part analysis of a system is a key element in a system reliability quantification process. It enables the weakest areas of a system to be recognized and assists in directing remedial measures for improving the system reliability. This paper presents a novel approach to identifying the weak parts using the unreliability tracing (UT) technique and introduces the proportional sharing principle (PSP). The model for tracing the unreliability of a complex network is presented based on reliability evaluation methods using minimal cut sets (MCSs) and the PSP. The system UT sharing factors (UTSFs) are derived to easily identify the major unreliability contributions (MUCs) in a system. The method is illustrated using three cases and the UT, UTSF and the reliability impact analysis of different components are discussed. The results show that the developed technique can be applied to complex networks for UT tracing and recognizing the MUC

[en] We explore the concepts of self-similarity, dimensionality, and (multi)scaling in a new family of recursive scale-free nets that yield themselves to exact analysis through renormalization techniques. All nets in this family are self-similar and some are fractals-possessing a finite fractal dimension-while others are small-world (their diameter grows logarithmically with their size) and are infinite-dimensional. We show how a useful measure of transfinite dimension may be defined and applied to the small-world nets. Concerning multiscaling, we show how first-passage time for diffusion and resistance between hubs (the most connected nodes) scale differently than for other nodes. Despite the different scalings, the Einstein relation between diffusion and conductivity holds separately for hubs and nodes. The transfinite exponents of small-world nets obey Einstein relations analogous to those in fractal nets

[en] We introduce a network growth model based on complete redirection: a new node randomly selects an existing target node, but attaches to a random neighbor of this target. For undirected networks, this simple growth rule generates unusual, highly modular networks. Individual network realizations typically contain multiple macrohubs—nodes whose degree scales linearly with the number of nodes N. The size of the network ‘nucleus’—the set of nodes of degree greater than one—grows sublinearly with N and thus constitutes a vanishingly small fraction of the network. The network therefore consists almost entirely of leaves (nodes of degree one) as $N\to <!--\; ???\; -->\mathrm{\infty <!--\; ???\; -->}$. (paper: interdisciplinary statistical mechanics)

[en] Complex networks have been widely studied recent years, but most researches focus on the single, non-interacting networks. With the development of modern systems, many infrastructure networks are coupled together and therefore should be modeled as interdependent networks. For interdependent networks, failure of nodes in one network may lead to failure of dependent nodes in the other networks. This may happen recursively and lead to a failure cascade. In the real world, different networks carry different traffic loads. Overload and load redistribution may lead to more nodes’ failure. Considering the dependency between the interdependent networks and the traffic load, a small fraction of fault nodes may lead to complete fragmentation of a system. Based on the robust analysis of interdependent networks, we propose a costless defense strategy to suppress the failure cascade. Our findings highlight the need to consider the load and coupling preference when designing robust interdependent networks. And it is necessary to take actions in the early stage of the failure cascade to decrease the losses caused by the large-scale breakdown of infrastructure networks. (paper)

[en] We propose a parametrized walk-based measure for the lack of balance in signed networks inspired by the Katz measure of similarity of two vertices in a network. We show that the performance of the proposed measure is marginally better than a recently proposed walk-based measure of the lack of balance for an undirected version of the real-world signed networks: Epinions, Slashdot and WikiElection. The proposed measure can be used to distinguish signed social networks on the basis of their degree of lack of balance. We also establish that cycles of shorter lengths can predict the sign of an edge in these signed networks better than the longer cycles by using the Katz prediction rule. (paper: disordered systems, classical and quantum)

[en] This paper investigates the finite-time generalized outer synchronization between two complex dynamical networks with different dynamical behaviors. The two networks can be undirected or directed, and they may also contain isolated nodes and clusters. By using suitable controllers, sufficient conditions for finite-time generalized outer synchronization are derived based on the finite-time stability theory. Finally, numerical examples are examined to illustrate the effectiveness of the analytical results. The effect of control parameters on the synchronization time is also numerically demonstrated.

[en] One important issue implied by the finite nature of real-world networks regards the identification of their more external (border) and internal nodes. The present work proposes a formal and objective definition of these properties, founded on the recently introduced concept of node diversity. It is shown that this feature does not exhibit any relevant correlation with several well-established complex networks measurements. A methodology for the identification of the borders of complex networks is described and illustrated with respect to theoretical (geographical and knitted networks) as well as real-world networks (urban and word association networks), yielding interesting results and insights in both cases.

[en] A goal of complex system research is to identify the dynamical implications of network structure. While early results focused mainly on local or global structural properties, there is now growing interest in mesoscale structures that comprise more than one node but not the whole network. A central challenge is to discover under what conditions the occurrence of a specific mesoscale motif already allows conclusions on the dynamics of a network as a whole. In this paper, we investigate the dynamics of ecological food webs, complex heterogeneous networks of interacting populations. Generalizing the results of MacArthur and Sánchez-García (2009 Phys. Rev. E 80 26117), we show that certain mesoscale symmetries imply the existence of localized dynamical modes. If these modes are unstable the occurrence of the corresponding mesoscale motif implies dynamical instability regardless of the structure of the embedding network. In contrast, if the mode is stable it means that the symmetry can be exploited to reduce the number of nodes in the model, without changing the dynamics of the system. This result explains a previously observed dynamical equivalence between food webs containing a different number of species. (paper)

[en] A model with a dynamical network structure is studied. The essential difference from other models is that a disappearance of links is also allowed. The obtained results suggest that under certain conditions a fairly robust cluster, which contains all of the elements of the system, can be formed. According to the power law dependence in the node connectivity distribution, a scale-free regime can occur in such models. The average network diameter behaves as K^-τ . The emergent structure is close to the small-world networks for certain values of p and to the large-world ones for others. Generally, the influence of the parameter K on the average network diameter is more significant than that of the systemsize