New trends on efficiency, vulnerability and cost for complex networks

The analysis of networks has become one of the paradigms of the science of complexity as well as a fascinating branch of research in applied mathematics, science and engineering: from the study of either biological networks to the Internet or the World Wide Web and other technological systems, as well as the study of social or economic relationships, to cite a sample, a detailed analysis of the underlying network is central for the modelling and understanding of the system behaviour. Such study requires the use of computable averaged magnitudes allowing a tractable approach to practical issues of description, analysis, design and optimization. Some of these parameters are the efficiency functions E(·) ([1, 3, 5]), vulnerabilities V (·) ([1, 2, 5]) and cost C(·) ([3, 5]). In this poster we present a systematic analysis of the structural correlations among these parameters for arbitrary kinds of complex networks. Specifically we also perform a random testing of these estimates applied to random graphs. This analysis extends and completes the results presented in [4].