We propose a dynamic network model where two mechanisms control the probability of a link between two nodes: (i) the existence or absence of this link in the past, and (ii) node-specific latent variables (dynamic fitnesses) describing the propensity of each node to create links. Assuming a Markov dynamics for both mechanisms, we propose an Expectation-Maximization algorithm for model estimation and inference of the latent variables. The estimated parameters and fitnesses can be used to forecast the presence of a link in the future. We apply our methodology to the e-MID interbank network for which the two linkage mechanisms are associated with two different trading behaviors in the process of network formation, namely preferential trading and trading driven by node-specific characteristics. The empirical results allow to recognise preferential lending in the interbank market and indicate how a method that does not account for time-varying network topologies tends to overestimate preferential linkage.

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In ATM systems, the massive number of interacting entities makes it difficult to predict the system-wide effects that innovations might have. Here, we present the approach proposed by the project Domino to assess and identify the impact that innovations might bring for the different stakeholders, based on agent-based modelling and complex network science. By investigating a dataset of US flights, we first show that existing centrality and causality metrics are not suited in characterising the effect of delays in the system. We then propose generalisations of such metrics that we prove suited to ATM applications. Then, we introduce the Agent Based Model used in Domino to model scenarios mirroring different system innovations which change the agents' actions and behaviour. We focus on a specific innovation related to flight arrival coordination and we show the insights on its effects at the network level obtained by applying the proposed new metrics.

In complex networks, centrality metrics quantify the connectivity of nodes and identify the most important ones in the transmission of signals. In many real world networks, especially in transportation systems, links are dynamic, i.e. their presence depends on time, and travelling between two nodes requires a non-vanishing time. Additionally, many networks are structured on several layers, representing, e.g., different transportation modes or service providers. Temporal generalisations of centrality metrics based on walk-counting, like Katz centrality, exist, however they do not account for non-zero link travel times and for the multiplex structure. We propose a generalisation of Katz centrality, termed Trip Centrality, counting only the walks that can be travelled according to the network temporal structure, i.e. “trips”, while also differentiating the contributions of inter- and intra-layer walks to centrality. We show an application to the US air transport system, specifically computing airports’ centrality losses due to delays in the flight network.

Betweenness centrality quantifies the importance of a vertex for the information flow in a network. The standard betweenness centrality applies to static single-layer networks, but many real world networks are both dynamic and made of several layers. We propose a definition of betweenness centrality for temporal multiplexes. This definition accounts for the topological and temporal structure and for the duration of paths in the determination of the shortest paths. We propose an algorithm to compute the new metric using a mapping to a static graph. We apply the metric to a dataset of $$\sim 20$$ ∼ 20 k European flights and compare the results with those obtained with static or single-layer metrics. The differences in the airports rankings highlight the importance of considering the temporal multiplex structure and an appropriate distance metric.