Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical consequences of these fixed observables, plus randomness in other respects. Here we employ the dk-series, a complete set of basic characteristics of the network structure, to study the statistical dependencies between different network properties. We consider six real networks—the Internet, US airport network, human protein interactions, technosocial web of trust, English word network, and an fMRI map of the human brain—and find that many important local and global structural properties of these networks are closely reproduced by dk-random graphs whose degree distributions, degree correlations and clustering are as in the corresponding real network. We discuss important conceptual, methodological, and practical implications of this evaluation of network randomness, and release software to generate dk-random graphs.
The objective of this article is to demonstrate the feasibility of on-demand creation of cloud-based elastic mobile core networks, along with their lifecycle management. For this purpose the article describes the key elements to realize the architectural vision of EPC as a Service, an implementation option of the Evolved Packet Core, as specified by 3GPP, which can be deployed in cloud environments. To meet several challenging requirements associated with the implementation of EPC over a cloud infrastructure and providing it "as a Service," this article presents a number of different options, each with different characteristics, advantages, and disadvantages. A thorough analysis comparing the different implementation options is also presented
Abstract-We study the algebraic connectivity in relation to the graph's robustness to node and link failures. Graph's robustness is quantified with the node and the link connectivity, two topological metrics that give the number of nodes and links that have to be removed in order to disconnect a graph. The algebraic connectivity, i.e. the second smallest eigenvalue of the Laplacian matrix, is a spectral property of a graph, which is an important parameter in the analysis of various robustness-related problems. In this paper we study the relationship between the proposed metrics in three well-known complex network models: the random graph of Erdős-Rényi, the smallworld graph of Watts-Strogatz and the scale-free graph of Barabási-Albert. From [11] it is known that the algebraic connectivity is a lower bound on both the node and the link connectivity. Through extensive simulations with the three complex network models, we show that the algebraic connectivity is not trivially connected to graph's robustness to node and link failures. Furthermore, we show that the tightness of this lower bound is very dependent on the considered complex network model.
Abstract-Comparing graphs to determine the level of underlying structural similarity between them is a widely encountered problem in computer science. It is particularly relevant to the study of Internet topologies, such as the generation of synthetic topologies to represent the Internet's AS topology. We derive a new metric that enables exactly such a structural comparison, the weighted spectral distribution. We then apply this metric to three aspects of the study of the Internet's AS topology. (i) we use it to quantify the effect of changing the mixing properties of a simple synthetic network generator. (ii) we use this quantitative understanding to examine the evolution of the Internet's AS topology over approximately 7 years, finding that the distinction between the Internet core and periphery has blurred over time.(iii) we use the metric to derive optimal parameterizations of several widely used AS topology generators with respect to a large-scale measurement of the real AS topology.
The second smallest eigenvalue of the Laplacian matrix, also known as the algebraic connectivity, plays a special role for the robustness of networks since it measures the extent to which it is difficult to cut the network into independent components. In this paper we study the behavior of the algebraic connectivity in a well-known complex network model, the Erdős-Rényi random graph. We estimate analytically the mean and the variance of the algebraic connectivity by approximating it with the minimum nodal degree. The resulting estimate improves a known expression for the asymptotic behavior of the algebraic connectivity [18]. Simulations emphasize the accuracy of the analytical estimation, also for small graph sizes. Furthermore, we study the algebraic connectivity in relation to the graph's robustness to node and link failures, i.e. the number of nodes and links that have to be removed in order to disconnect a graph. These two measures are called the node and the link connectivity. Extensive simulations show that the node and the link connectivity converge to a distribution identical to that of the minimal nodal degree, already at small graph sizes. This makes the minimal nodal degree a valuable estimate of the number of nodes or links whose deletion results into disconnected random graph. Moreover, the algebraic connectivity increases with the increasing node and link connectivity, justifies the correctness of our definition that the algebraic connectivity is a measure of the robustness in complex networks.
Over the past several years, a number of measures have been introduced to characterize the topology of complex networks. We perform a statistical analysis of real data sets, representing the topology of different realworld networks. First, we show that some measures are either fully related to other topological measures or that they are significantly limited in the range of their possible values. Second, we observe that subsets of measures are highly correlated, indicating redundancy among them. Our study thus suggests that the set of commonly used measures is too extensive to concisely characterize the topology of complex networks. It also provides an important basis for classification and unification of a definite set of measures that would serve in future topological studies of complex networks.
Abstract-In this paper we study the spectral radius of a number of real-life networks. This study is motivated by the fact that the smaller the spectral radius, the higher the robustness of a network against the spread of viruses. First we study how wellknown upper bounds for the spectral radius of graphs match to the spectral radii of the social network of the Dutch soccer team, the Dutch roadmap network, the network of the observable part of the Internet graph at the IP-level and the Autonomous System level. Secondly, we compare the spectral radius for these real-life networks with those of commonly used complex network models.
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