http://www.maths.qmul.ac.uk/%7Elatora/report_06.pdf

Complex networks: Structure and dynamics

Complex networks have been studied intensively for a decade, but research still focuses on the limited case of a single, non-interacting network. Modern systems are coupled together and therefore should be modelled as interdependent networks. A fundamental property of interdependent networks is that failure of nodes in one network may lead to failure of dependent nodes in other networks. This may happen recursively and can lead to a cascade of failures. In fact, a failure of a very small fraction of nodes in one network may lead to the complete fragmentation of a system of several interdependent networks. A dramatic real-world example of a cascade of failures ('concurrent malfunction') is the electrical blackout that affected much of Italy on 28 September 2003: the shutdown of power stations directly led to the failure of nodes in the Internet communication network, which in turn caused further breakdown of power stations. Here we develop a framework for understanding the robustness of interacting networks subject to such cascading failures. We present exact analytical solutions for the critical fraction of nodes that, on removal, will lead to a failure cascade and to a complete fragmentation of two interdependent networks. Surprisingly, a broader degree distribution increases the vulnerability of interdependent networks to random failure, which is opposite to how a single network behaves. Our findings highlight the need to consider interdependent network properties in designing robust networks.

/pdf/catastrophic-cascade-of-failures-in-interdependent-networks-414vwz21eb.pdf

Catastrophic cascade of failures in interdependent networks

Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of complex networks therefore rely on the use of measurements capable of expressing the most relevant topological features. This article presents a survey of such measurements. It includes general considerations about complex network characterization, a brief review of the principal models, and the presentation of the main existing measurements. Important related issues covered in this work comprise the representation of the evolution of complex networks in terms of trajectories in several measurement spaces, the analysis of the correlations between some of the most traditional measurements, perturbation analysis, as well as the use of multivariate statistics for feature selection and network classification. Depending on the network and the analysis task one has in mind, a s...

https://arxiv.org/pdf/cond-mat/0505185.pdf

Characterization of complex networks: A survey of measurements

Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of complex networks therefore rely on the use of measurements capable of expressing the most relevant topological features. This article presents a survey of such measurements. It includes general considerations about complex network characterization, a brief review of the principal models, and the presentation of the main existing measurements. Important related issues covered in this work comprise the representation of the evolution of complex networks in terms of trajectories in several measurement spaces, the analysis of the correlations between some of the most traditional measurements, perturbation analysis, as well as the use of multivariate statistics for feature selection and network classification. Depending on the network and the analysis task one has in mind, a specific set of features may be chosen. It is hoped that the present survey will help the proper application and interpretation of measurements.

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications Such systems include multiple subsystems and layers of connectivity, and it is important to take such "multilayer" features into account to try to improve our understanding of complex systems Consequently, it is necessary to generalize "traditional" network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other, and provide a thorough discussion that compares, contrasts, and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks, and many others We also survey and discuss existing data sets that can be represented as multilayer networks We review attempts to generalize single-layer-network diagnostics to multilayer networks We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions, and various types of dynamical processes on multilayer networks We conclude with a summary and an outlook

Multilayer Networks

We investigate the consequence of failures, occurring on the electrical grid, on a telecommunication network We have focused on the Italian electrical transmission network and the backbone of the internet network for research (GARR) Electrical network has been simulated using the DC power flow method; data traffic on GARR by a model of the TCP/IP basic features The status of GARR nodes has been related to the power level of the (geographically) neighbouring electrical nodes (if the power level of a node is lower than a threshold, all communication nodes depending on it are switched off) The electrical network has been perturbed by lines removal: the consequent re-dispatching reduces the power level in all nodes This reduces the number of active GARR nodes and, thus, its Quality of Service (QoS) Averaging over many configurations of perturbed electrical network, we have correlated the degradation of the electrical network with that of the communication network Results point to a sizeable amplification of the effects of faults on the electrical network on the communication network, also in the case of a moderate coupling between the two networks

Modelling interdependent infrastructures using interacting dynamical models

Topological properties of high-voltage electrical transmission networks

The Internet is one of the most interesting realizations of a “complex” network. As a non-supervised growing object, it allows the study of the selective pressure which drives the network to assume its current structure. The DIMES and the ROUTEVIEWS projects are ongoing projects aimed at evaluating the topological structure of the Internet (at the Autonomous System or AS grain-level) on the basis of different types of measurements. The topological analysis of the networks produced by the two projects has allowed us to infer a growth mechanism which has been used to build up synthetic networks with similar properties. These networks have been used as test-beds for the implementation of a model of traffic dynamics, with the aim of assessing the ability of the Internet’s topology to support the basic actions for data traffic handling. Results have been compared with those obtained by using a random network of similar size. The effects of some structural perturbations (arcs and nodes’ removal, traffic localization) have been also evaluated in terms of the induced variations of the network’s efficiency. The resulting scenario is consistent with the hypothesis that the structure of the Internet is only partially fit to host communication processes and that the intelligence of the TCP/IP protocol is partly needed to overcome some “structural” deficiencies.

Is the topology of the internet network really fit to sustain its function

The growth of the AS (Autonomous System) level router network has been analyzed during a period of almost two years (1998–2000). The behavior of the clustering coefficient and that of the "min-cut" analysis on the network have been used as key features to simulate the network growth. The Triad Formation mechanism, which suitably incorporates also the Preferential Attachment mechanism, is an adequate recipe for reproducing relevant structural properties of the AS-level router network during its stages of growth.

F. Tiriticco

Papers

Modelling interdependent infrastructures using interacting dynamical models

Topological properties of high-voltage electrical transmission networks

Is the topology of the internet network really fit to sustain its function

Growth mechanisms of the AS-level Internet network