The interplay between disease dynamics on a network and the dynamics of the structure of that network characterizes many real-world systems of contacts. A continuous-time adaptive susceptible-infectious-susceptible (ASIS) model is introduced in order to investigate this interaction, where a susceptible node avoids infections by breaking its links to its infected neighbors while it enhances the connections with other susceptible nodes by creating links to them. When the initial topology of the network is a complete graph, an exact solution to the average metastable-state fraction of infected nodes is derived without resorting to any mean-field approximation. A linear scaling law of the epidemic threshold τ c as a function of the effective link-breaking rate ω is found. Furthermore, the bifurcation nature of the metastable fraction of infected nodes of the ASIS model is explained. The metastable-state topology shows high connectivity and low modularity in two regions of the τ,ω plane for any effective infection rate τ > τ c : (i) a "strongly adaptive" region with very high ω and (ii) a "weakly adaptive" region with very low ω. These two regions are separated from the other half-open elliptical-like regions of low connectivity and high modularity in a contour-line-like way. Our results indicate that the adaptation of the topology in response to disease dynamics suppresses the infection, while it promotes the network evolution towards a topology that exhibits assortative mixing, modularity, and a binomial-like degree distribution.

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Transmission efficiency and robustness are two important properties of various networks and a number of optimization strategies have been proposed recently. We propose a scheme to enhance the network performance by adding a small fraction of links (or edges) to the currently existing network topology, and we present four edge addition strategies for adding edges efficiently. We aim at minimizing the maximum node betweenness of any node in the network to improve its transmission efficiency, and a number of experiments on both Barab asiÀAlbert (BA) and Erd€ osÀR enyi (ER) networks have confirmed the effectiveness of our four edge addition strategies. Also, we evaluate the effect of some other measure metrics such as average path length, average betweenness, robustness, and degree distribution. Our work is very valuable and helpful for service providers to optimize their network performance by adding a small fraction of edges or to make good network planning on the existing network topology incrementally.

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The continuous-time adaptive susceptible-infected-susceptible (ASIS) epidemic model and the adaptive information diffusion (AID) model are two adaptive spreading processes on networks, in which a link in the network changes depending on the infectious state of its end nodes, but in opposite ways: (i) In the ASIS model a link is removed between two nodes if exactly one of the nodes is infected to suppress the epidemic, while a link is created in the AID model to speed up the information diffusion; (ii) a link is created between two susceptible nodes in the ASIS model to strengthen the healthy part of the network, while a link is broken in the AID model due to the lack of interest in informationless nodes. The ASIS and AID models may be considered as first-order models for cascades in real-world networks. While the ASIS model has been exploited in the literature, we show that the AID model is realistic by obtaining a good fit with Facebook data. Contrary to the common belief and intuition for such similar models, we show that the ASIS and AID models exhibit different but not opposite properties. Most remarkably, a unique metastable state always exists in the ASIS model, while there an hourglass-shaped region of instability in the AID model. Moreover, the epidemic threshold is a linear function in the effective link-breaking rate in the AID model, while it is almost constant but noisy in the AID model. Over the past decade, many real-world networks have been characterized via graph metrics [1-3] such as clustering, assortativity, modularity, degree distribution, and spectral properties. Recently, robustness characteristics and complex dependences have been analyzed in networks of networks [4], while a parallel track in network science has focused on relatively simple dynamic processes on networks such as epidemics [5,6], synchronization [7], and opinion diffusion [8][9][10]. In most studies so far, the networks are considered fixed or independent of the dynamic process. After the seminal work of Gross et al. [11], the coupling between epidemic processes and the underlying network topology has been extensively studied [12][13][14][15].The coupling between process and topology is natural in many cases. In epidemics [16], for example, after the observation of an infectious relative, one may either avoid him or her (by changing the social contact network) or increase the protection against the virus (without altering the topology). In human brain networks, Hebbian learning alters the connectivity between brain regions that are trained or neurally excited. Although self-adaptation naturally occurs in biology, adaptive networks, in which the process interacts with the topology, are unfortunately difficult to analyze and we barely understand the interplay between process and topology. Twitter measurements [17,18] show that the topology of the network adaptively changes connectivity towards users with high popularity and the ordinary users tend to directly follow the popular ones to get the information faster, instead of a...

Considering the heterogeneous structure of scale-free networks causing low traffic capacity of network, we propose to improve the network transport efficiency by rewiring a fraction of edges for the network. In this paper, six edge rewiring strategies are discussed and extensive simulations on Barabási–Albert (BA) scale-free networks confirm the effectiveness of these strategies. From another perspective, rewiring edges for scale-free networks directly reuse the removed edges under some edge-removal strategies [Z. Liu, M. B. Hu, R. Jiang, W. X. Wang and Q. S. Wu, Phys. Rev. E76 (2007) 037101; G. Q. Zhang, D. Wang and G. J. Li, Phys. Rev. E76 (2007) 017101], and can significantly enhance the traffic capacity of the network at the expense of increasing a little average path length. After the edge rewiring process, the network structure becomes significantly homogeneous. This work is helpful for network design and network performance optimization.

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