A new design principle of robust onion-like networks self-organized in growth

Today's economy, production activity, and our life are sustained by social and technological network infrastructures, while new threats of network attacks by destructing loops have been found recently in network science. We inversely take into account the weakness, and propose a new design principle for incrementally growing robust networks. The networks are self-organized by enhancing interwoven long loops. In particular, we consider the range-limited approximation of linking by intermediations in a few hops, and show the strong robustness in the growth without degrading efficiency of paths. Moreover, we demonstrate that the tolerance of connectivity is reformable even from extremely vulnerable real networks according to our proposed growing process with some investment. These results may indicate a prospective direction to the future growth of our network infrastructures.Comment: 21 pages, 10 figures, 1 tabl

An approximative calculation of the fractal structure in self-similar tilings

Fractal structures emerge from statistical and hierarchical processes in urban development or network evolution. In a class of efficient and robust geographical networks, we derive the size distribution of layered areas, and estimate the fractal dimension by using the distribution without huge computations. This method can be applied to self-similar tilings based on a stochastic process.Comment: 5 pages, 6 figure

Simple Derivation of the Lifetime and the Distribution of Faces for a Binary Subdivision Model

The iterative random subdivision of rectangles is used as a generation model of networks in physics, computer science, and urban planning. However, these researches were independent. We consider some relations in them, and derive fundamental properties for the average lifetime depending on birth-time and the balanced distribution of rectangle faces.Comment: 2 figure

Recoverable DTN Routing based on a Relay of Cyclic Message-Ferries on a MSQ Network

An interrelation between a topological design of network and efficient algorithm on it is important for its applications to communication or transportation systems. In this paper, we propose a design principle for a reliable routing in a store-carry-forward manner based on autonomously moving message-ferries on a special structure of fractal-like network, which consists of a self-similar tiling of equilateral triangles. As a collective adaptive mechanism, the routing is realized by a relay of cyclic message-ferries corresponded to a concatenation of the triangle cycles and using some good properties of the network structure. It is recoverable for local accidents in the hierarchical network structure. Moreover, the design principle is theoretically supported with a calculation method for the optimal service rates of message-ferries derived from a tandem queue model for stochastic processes on a chain of edges in the network. These results obtained from a combination of complex network science and computer science will be useful for developing a resilient network system.Comment: 6 pages, 12 figures, The 3rd Workshop on the FoCAS(Fundamentals of Collective Adaptive Systems) at The 9th IEEE International Conference on SASO(Self-Adaptive and Self-Organizing systems), Boston, USA, Sept.21, 201

Asymptotic behavior of the node degrees in the ensemble average of adjacency matrix

Various important and useful quantities or measures that characterize the topological network structure are usually investigated for a network, then they are averaged over the samples. In this paper, we propose an explicit representation by the beforehand averaged adjacency matrix over samples of growing networks as a new general framework for investigating the characteristic quantities. It is applied to some network models, and shows a good approximation of degree distribution asymptotically. In particular, our approach will be applicable through the numerical calculations instead of intractable theoretical analysises, when the time-course of degree is a monotone increasing function like power-law or logarithm.Comment: 13 paghes, 7 figure

Spatially self-organized resilient networks by a distributed cooperative mechanism

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.Comment: 34 pages, 12 figures, 2 table