[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] 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] 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] 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] The identification of influential nodes in complex networks is one of the most exciting topics in network science. The latest work successfully compares each node using local connectivity and weak tie theory from a new perspective. We study the structural properties of networks in depth and extend this successful node evaluation from single-scale to multi-scale. In particular, one novel position parameter based on node transmission efficiency is proposed, which mainly depends on the shortest distances from target nodes to high-degree nodes. In this regard, the novel multi-scale information importance (MSII) method is proposed to better identify the crucial nodes by combining the network’s local connectivity and global position information. In simulation comparisons, five state-of-the-art algorithms, i.e. the neighbor nodes degree algorithm (NND), betweenness centrality, closeness centrality, Katz centrality and the k-shell decomposition method, are selected to compare with our MSII. The results demonstrate that our method obtains superior performance in terms of robustness and spreading propagation for both real-world and artificial networks. (paper)

[en] In this paper, we study noisy consensus dynamics in two families of weighted ring-trees networks and recursive trees with a controlled initial state. Based on the topological structures, we obtain exact expressions for the first- and second-order network coherence as a function of the involved parameters and provide the scalings of network coherence regarding network size. We then show that the weights dominate the consensus behaviors and the scalings. Finally, we make a comparison of the network coherence between the ring-trees networks and the recursive trees with the same number of nodes and show that the consensus of ring-trees networks is better than the trees since the initial state in the ring-trees networks is a ring. (paper)

[en] We use the controllability limit theory to study impact of correlation between in- and out-degrees (degree correlation) on edge controllability of real networks. Simulation results and analytic calculations show that the degree correlation plays an important role in the edge controllability of real networks, especially dense real networks. The upper and lower controllability limits hold for all kinds of real networks. Any edge controllability in between the limits is achievable by properly adjusting the degree correlation. In addition, we find that the edge dynamics in some real networks with positive degree correlation may be difficult to control, and explain the rationality of this anomaly based on the controllability limit theory. (paper)

[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.