Massimiliano Zanin

The structure and dynamics of multilayer networks

n Abstractn n In the past years, network theory has successfully characterized the interaction among the constituents of a variety of complex systems, ranging from biological to technological, and social systems. However, up until recently, attention was almost exclusively given to networks in which all components were treated on equivalent footing, while neglecting all the extra information about the temporal- or context-related properties of the interactions under study. Only in the last years, taking advantage of the enhanced resolution in real data sets, network scientists have directed their interest to the multiplex character of real-world systems, and explicitly considered the time-varying and multilayer nature of networks. We offer here a comprehensive review on both structural and dynamical organization of graphs made of diverse relationships (layers) between its constituents, and cover several relevant issues, from a full redefinition of the basic structural measures, to understanding how the multilayer nature of the network affects processes and dynamics.n n

Modelling the air transport with complex networks: A short review

Air transport is a key infrastructure of modern societies. In this paper we review some recent approaches to air transport, which make extensive use of theory of complex networks. We discuss possible networks that can be defined for the air transport and we focus our attention to networks of airports connected by flights. We review several papers investigating the topology of these networks and their dynamics for time scales ranging from years to intraday intervals, and consider also the resilience properties of air networks to extreme events. Finally we discuss the results of some recent papers investigating the dynamics on air transport network, with emphasis on passengers traveling in the network and epidemic spreading.

Functional brain networks: great expectations, hard times and the big leap forward

Many physical and biological systems can be studied using complex network theory, a new statistical physics understanding of graph theory. The recent application of complex network theory to the study of functional brain networks has generated great enthusiasm as it allows addressing hitherto non-standard issues in the field, such as efficiency of brain functioning or vulnerability to damage. However, in spite of its high degree of generality, the theory was originally designed to describe systems profoundly different from the brain. We discuss some important caveats in the wholesale application of existing tools and concepts to a field they were not originally designed to describe. At the same time, we argue that complex network theory has not yet been taken full advantage of, as many of its important aspects are yet to make their appearance in the neuroscience literature. Finally, we propose that, rather than simply borrowing from an existing theory, functional neural networks can inspire a fundamental reformulation of complex network theory, to account for its exquisitely complex functioning mode.

Combining complex networks and data mining: Why and how

The increasing power of computer technology does not dispense with the need to extract meaningful in- formation out of data sets of ever growing size, and indeed typically exacerbates the complexity of this task. To tackle this general problem, two methods have emerged, at chronologically different times, that are now commonly used in the scientific community: data mining and complex network theory. Not only do complex network analysis and data mining share the same general goal, that of extracting information from complex systems to ultimately create a new compact quantifiable representation, but they also often address similar problems too. In the face of that, a surprisingly low number of researchers turn out to resort to both methodologies. One may then be tempted to conclude that these two fields are either largely redundant or totally antithetic. The starting point of this review is that this state of affairs should be put down to contingent rather than conceptual differences, and that these two fields can in fact advantageously be used in a synergistic manner. An overview of both fields is first provided, some fundamental concepts of which are illustrated. A variety of contexts in which complex network theory and data mining have been used in a synergistic manner are then presented. Contexts in which the appropriate integration of complex network metrics can lead to improved classification rates with respect to classical data mining algorithms and, conversely, contexts in which data mining can be used to tackle important issues in complex network theory applications are illustrated. Finally, ways to achieve a tighter integration between complex networks and data mining, and open lines of research are discussed.

Can we neglect the multi-layer structure of functional networks?

Functional networks, i.e. networks representing dynamic relationships between the components of a complex system, have been instrumental for our understanding of, among others, the human brain. Due to limited data availability, the multi-layer nature of numerous functional networks has hitherto been neglected, and nodes are endowed with a single type of links even when multiple relationships coexist at different physical levels. A relevant problem is the assessment of the benefits yielded by studying a multi-layer functional network, against the simplicity guaranteed by the reconstruction and use of the corresponding single layer projection. Here, I tackle this issue by using as a test case, the functional network representing the dynamics of delay propagation through European airports. Neglecting the multi-layer structure of a functional network has dramatic consequences on our understanding of the underlying system, a fact to be taken into account when a projection is the only available information.

Dynamics in scheduled networks

When studying real or virtual systems through complex networks theories, usually time restrictions are neglected, and a static structure is defined to characterize which node is connected to which other. However, this approach is oversimplified, as real networks are indeed dynamically modified by external mechanisms. In order to bridge the gap, in this work we present a scheduled network formalism, which takes into account such dynamical modifications by including generic time restrictions in the structure of an extended adjacency matrix. We present some of its properties and apply this formalism to the specific case of the air transportation network in order to analyze its efficiency. Real data are used at this point. We finally discuss on the applicability of this formalism to other complex systems.

Beware of the Small-World Neuroscientist!

Characterizing the brains anatomical and dynamical organization and how this enables it to carry out complex tasks is highly non trivial. While there has long been strong evidence that brain anatomy can be thought of as a complex network at micro as well as macro scales, the use of functional imaging techniques has recently shown that brain dynamics also has a network-like structure.

QRE: Quick Robustness Estimation for large complex networks

Abstract Robustness estimation is critical for the design and maintenance of resilient networks. Existing studies on network robustness usually exploit a single network metric to generate attack strategies, which simulate intentional attacks on a network, and compute a metric-induced robustness estimation, called R . While some metrics are easy to compute, e.g. degree, others require considerable computation efforts, e.g. betweenness centrality. We propose Quick Robustness Estimation (QRE), a new framework and implementation for estimating the robustness of a network in sub-quadratic time, i.e., significantly faster than betweenness centrality, based on the combination of cheap-to-compute network metrics. Experiments on twelve real-world networks show that QRE estimates the robustness better than betweenness centrality-based computation, while being at least one order of magnitude faster for larger networks. Our work contributes towards scalable, yet accurate robustness estimation for large complex networks.

Reconstructing functional brain networks: have we got the basics right?

Both at rest and during the executions of cognitive tasks, the brain continuously creates and reshapes complex patterns of correlated dynamics. Thus, brain functional activity is naturally described in terms of networks, i.e., sets of nodes, representing distinct subsystems, and links connecting node pairs, representing relationships between them. n nRecently, brain function has started being investigated using a statistical physics understanding of graph theory, an old branch of pure mathematics (Newman, 2010). Within this framework, network properties are independent of the identity of their nodes, as they emerge in a non-trivial way from their interactions. Observed topologies are instances of a network ensemble, falling into one of few universality classes and are therefore inherently statistical in nature. n nFunctional network reconstruction comprises various steps: first, nodes are identified; then, links are established according to a certain metric. This gives rise to a clique with an all-to-all connectivity. Deciding which links are significant is done by choosing which values of these metrics should be taken into account. Finally, network properties are computed and used to characterize the network. n nEach of these steps contains an element of arbitrariness, as graph theory allows characterizing systems once a network is reconstructed, but is neutral as to what should be treated as a system and to how to isolate its constituent parts. n nHere we discuss some aspects related to the way nodes, links and networks in general are defined in system-level studies using noninvasive techniques, which may be critical when interpreting the results of functional brain network analyses.

Worldwide air transportation networks: a matter of scale and fractality?

ABSTRACT In this study, we take a new view on air transportation networks, inspired by the physical concept of fractality. While other studies analyze networks individually, we aim to provide a unified understanding of the transitions among network layers. As a case study, we investigate the worldwide air transportation networks for the year 2015. We derive aggregated network instances at six different levels: airports, cities, spatial distance 100u2009km, spatial distance 200u2009km, regional network, and country network. While few nodes are important at all levels of aggregation, others only become important for few aggregation levels. Fractality analysis highlights that, as one moves from finer granularity to more coarse aggregation level, the network becomes denser but with fluctuating assortativity patterns; and that the modularity and the number of communities both decrease slightly. Networks at higher aggregation levels are more robust than the fine-grained counterparts, airport and city networks.