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Register a new userSpatially self-organized resilient networks by a distributed cooperative mechanism
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Authors
Yukio Hayashi
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The robustness of connectivity and the efficiency of paths are incompatible in many real networks. We propose a self-organization mechanism for incrementally generating onion-like networks with positive degree-degree correlations whose robustness is nearly optimal. As a spatial extension of the generation model based on cooperative copying and adding shortcut, we show that the growing networks become more robust and efficient through enhancing the onion-like topological structure on a space. The reasonable constraint for locating nodes on the perimeter in typical surface growth as a self-propagation does not affect these properties of the tolerance and the path length. Moreover, the robustness can be recovered in the random growth damaged by insistent sequential attacks even without any remedial measures.
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A self-organization of efficient and robust networks is important for a future design of communication or transportation systems, however both characteristics are incompatible in many real networks. Recently, it has been found that the robustness of onion-like structure with positive degree-degree correlations is optimal against intentional attacks. We show that, by biologically inspired copying, an onion-like network emerges in the incremental growth with functions of proxy access and reinforced connectivity on a space. The proposed network consists of the backbone of tree-like structure by copyings and the periphery by adding shortcut links between low degree nodes to enhance the connectivity. It has the fine properties of the statistically self-averaging unlike the conventional duplication-divergence model, exponential-like degree distribution without overloaded hubs, strong robustness against both malicious attacks and random failures, and the efficiency with short paths counted by the number of hops as mediators and by the Euclidean distances. The adaptivity to heal over and to recover the performance of networking is also discussed for a change of environment in such disasters or battlefields on a geographical map. These properties will be useful for a resilient and scalable infrastructure of network systems even in emergent situations or poor environments.
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We propose a bare-bones stochastic model that takes into account both the geographical distribution of people within a country and their complex network of connections. The model, which is designed to give rise to a scale-free network of social connections and to visually resemble the geographical spread seen in satellite pictures of the Earth at night, gives rise to a power-law distribution for the ranking of cities by population size (but for the largest cities) and reflects the notion that highly connected individuals tend to live in highly populated areas. It also yields some interesting insights regarding Gibrats law for the rates of city growth (by population size), in partial support of the findings in a recent analysis of real data [Rozenfeld et al., Proc. Natl. Acad. Sci. U.S.A. 105, 18702 (2008)]. The model produces a nontrivial relation between city population and city population density and a superlinear relationship between social connectivity and city population, both of which seem quite in line with real data.
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