We consider normalized average edge betweenness of a network as a metric of network vulnerability. We suggest that normalized average edge betweenness together with is relative difference when certain number of nodes and/or edges are removed from the network is a measure of network vulnerability, called vulnerability index. Vulnerability index is calculated for four synthetic networks: Erdös-Rényi (ER) random networks, Barabási-Albert (BA) model of scale-free networks, Watts-Strogatz (WS) model of small-world networks, and geometric random networks. Real-world networks for which vulnerability index is calculated include: two human brain networks, three urban networks, one collaboration network, and two power grid networks. We find that WS model of small-world networks and biological networks (human brain networks) are the most robust networks among all networks studied in the paper.
Synchronization is deemed to play an important role in information processing in many neuronal systems. In this work, using a well known technique due to Pecora and Carroll, we investigate the existence of a synchronous state and the bifurcation diagram of a network of synaptically coupled neurons described by the Hindmarsh-Rose model. Through the analysis of the bifurcation diagram, the different dynamics of the possible synchronous states are evidenced. Furthermore, the influence of the topology on the synchronization properties of the network is shown through an example.
SUMMARYA CNN model of partial di erential equations (PDEs) for image multiscale analysis is proposed. The model is based on a polynomial representation of the di usivity function and deÿnes a paradigm of polynomial CNNs, for approximating a large class of non-linear isotropic and=or anisotropic PDEs. The global dynamics of space-discrete polynomial CNN models is analysed and compared with the dynamic behaviour of the corresponding space-continuous PDE models. It is shown that in the isotropic case the two models are not topologically equivalent; in particular, discrete CNN models allow one to obtain the output image without stopping the image evolution after a given time (scale). This property represents an advantage with respect to continuous PDE models and could simplify some image preprocessing algorithms.
In this paper we present a simple, fast, novel algorithm for building networks whose topology has high synchronizability, is robust against failures, and supports efficient communication. We show that the algorithm is able to build these networks in a small number of steps that scales with the networks density. In addition, we track the evolution of different topological properties in the process of generating these networks. The results show that the topological properties are homogeneously distributed and the topology is less authoritative. Furthermore, we show that the networks we generate are more robust than random, geometric random, small-world or scalefree networks with similar average connectivity. Finally, all of the results indicate that the topology of these networks is entangled, which in many cases represents an optimal topology.
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