Carlo Piccardi

With the impressive growth of network models in practically every scientific and technological area, we are often faced with the need to compare graphs, i.e., to quantify their (dis)similarity using appropriate metrics. This is necessary, for example, to identify networks with comparable characteristics or to spot anomalous instants in a time sequence of graphs. While a large number of metrics are available for binary networks, the set of comparison methods capable of handling weighted graphs is much smaller. Yet, the strength of connections is often a key ingredient of the model, and ignoring this information could lead to misleading results. In this paper we introduce a family of dissimilarity measures to compare undirected weighted networks. They fall into the class of alignment-free metrics: as such, they do not require the correspondence of the nodes between the two graphs and can also compare networks of different sizes. In short, they are based on the distributions, on the graph, of a few egonet features which are easily defined and computed: the distance between two graphs is then the distance between the corresponding distributions. On a properly defined testbed with a pool of weighted network models with diversified characteristics, the proposed metrics are shown to achieve state-of-the-art performance in the model classification task. The effectiveness and applicability of the proposed metrics are then demonstrated on two examples. In the first, some ”filtering” schemes – designed to eliminate non-significant links while maintaining most of the total weight – are evaluated in their ability to produce as output a graph faithful to the original, in terms of the local structure around nodes. In the second example, analyzing a timeline of stock market correlation graphs highlights anomalies associated with periods of financial instability.

Identifying networks with similar characteristics in a given ensemble, or detecting pattern discontinuities in a temporal sequence of networks, are two examples of tasks that require an effective metric capable of quantifying network (dis)similarity. Here we propose a method based on a global portrait of graph properties built by processing local nodes features. More precisely, a set of dissimilarity measures is defined by elaborating the distributions, over the network, of a few egonet features, namely the degree, the clustering coefficient, and the egonet persistence. The method, which does not require the alignment of the two networks being compared, exploits the statistics of the three features to define one- or multi-dimensional distribution functions, which are then compared to define a distance between the networks. The effectiveness of the method is evaluated using a standard classification test, i.e., recognizing the graphs originating from the same synthetic model. Overall, the proposed distances have performances comparable to the best state-of-the-art techniques (graphlet-based methods) with similar computational requirements. Given its simplicity and flexibility, the method is proposed as a viable approach for network comparison tasks.

Identifying networks with similar characteristics in a given ensemble, or detecting pattern discontinuities in a temporal sequence of networks, are two examples of tasks that require an effective metric capable of quantifying network (dis)similarity. Here we propose a method based on a global portrait of graph properties built by processing local nodes features. More precisely, a set of dissimilarity measures is defined by elaborating the distributions, over the network, of a few egonet features, namely the degree, the clustering coefficient, and the egonet persistence. The method, which does not require the alignment of the two networks being compared, exploits the statistics of the three features to define one- or multi-dimensional distribution functions, which are then compared to define a distance between the networks. The effectiveness of the method is evaluated using a standard classification test, i.e., recognizing the graphs originating from the same synthetic model. Overall, the proposed distances have performances comparable to the best state-of-the-art techniques (graphlet-based methods) with similar computational requirements. Given its simplicity and flexibility, the method is proposed as a viable approach for network comparison tasks.

Online social media have been one of the greatest drivers of societal change of the past two decades, but are now being recognized as one of the major causes of opinion radicalization and one of the most effective tools for opinion manipulation. Starting from a class of stochastic models of opinion dynamics, and considering different structures of social networks with increasingly realistic features (including a snapshot of the Facebook friendship network), we develop a mathematical model of different forms of opinion manipulation. We then explore how network properties, and in particular degree distribution and community structure, interact with the attack to amplify or reduce its effect on the population, both globally and on specific subsets. We find, in particular, that degree heterogeneity is key to making online social media susceptible to very effective attacks, even with relatively little effort. Communities instead play a more complex role, acting both as barriers to the spread of manipulated opinions through the whole population and as amplifiers of manipulated opinions when the target of the attack is a community of the online social medium. The results of our study can help design effective strategies to prevent the manipulation of opinions through online social media.

In recent years, the global trade landscape has undergone significant changes, particularly in the aftermath of the 2008 financial crisis and more recently as a consequence of Covid-19 pandemic. To understand the structure of international trade and the impact of these changes, this study applies a combination of network analysis and causal inference techniques to the most extensive coverage of available data in terms of time span and spatial extension. The study is conducted in two phases. The first one explores the structure of international trade by providing a comprehensive analysis of the World Trade Network (WTN) from various perspectives, including the identification of key players and clusters of strongly interacting countries. The second phase investigates the impact of the rising role of China on the global structure of the WTN. Overall, the results highlight a structural change in the WTN, evidenced by a variety of network metrics, around China’s rapid growth years. Additionally, the reshaping of the WTN is not only accompanied by a significant increase in trade flows between China and its partners, but also by a corresponding decline in trade among non-China-partner countries. These results suggest that China played a pivotal role in the restructuring of the WTN in the first decades of this century. The findings of this study shed light on the interpretation of the rapidly changing landscape of global trade.

While the share of services in international trade has been increasing very slowly over the years, oscillating around 20 per cent since the 1990s, their role has constantly gained importance. Trade in services certainly faces many more obstacles than trade in goods, but its impact on globalization and countries’ competitiveness is crucial, and it is therefore worth investigating its characteristics. The present work aims to analyse the networks of international trade in services and to unveil specific properties by exploiting a number of existing methodologies and algorithms. After describing the global properties of the networks of the various service classes, we investigate differences and similarities among them, and we highlight the most influential countries in the trade of specific services. We find that traded services display sharply different characteristics and they can be grouped in two different sets according to their network structures. Countries’ positions in these networks are diversified, with connections unevenly distributed, especially for some service categories. We discover that the structure of links, i.e. the topology of the networks, identifies the role of countries much more clearly than the sole amount of services traded. Overall, the results highlight important features, as well as changes over time, in the landscape of the international services.

In recent years, malicious information had an explosive growth in social media, with serious social and political backlashes. Recent important studies, featuring large-scale analyses, have produced deeper knowledge about this phenomenon, showing that misleading information spreads faster, deeper and more broadly than factual information on social media, where echo chambers, algorithmic and human biases play an important role in diffusion networks. Following these directions, we explore the possibility of classifying news articles circulating on social media based exclusively on a topological analysis of their diffusion networks. To this aim we collected a large dataset of diffusion networks on Twitter pertaining to news articles published on two distinct classes of sources, namely outlets that convey mainstream, reliable and objective information and those that fabricate and disseminate various kinds of misleading articles, including false news intended to harm, satire intended to make people laugh, click-bait news that may be entirely factual or rumors that are unproven. We carried out an extensive comparison of these networks using several alignment-free approaches including basic network properties, centrality measures distributions, and network distances. We accordingly evaluated to what extent these techniques allow to discriminate between the networks associated to the aforementioned news domains. Our results highlight that the communities of users spreading mainstream news, compared to those sharing misleading news, tend to shape diffusion networks with subtle yet systematic differences which might be effectively employed to identify misleading and harmful information.

With the impressive growth of available data and the flexibility of network modelling, the problem of devising effective quantitative methods for the comparison of networks arises. Plenty of such methods have been designed to accomplish this task: most of them deal with undirected and unweighted networks only, but a few are capable of handling directed and/or weighted networks too, thus properly exploiting richer information. In this work, we contribute to the effort of comparing the different methods for comparing networks and providing a guide for the selection of an appropriate one. First, we review and classify a collection of network comparison methods, highlighting the criteria they are based on and their advantages and drawbacks. The set includes methods requiring known node-correspondence, such as DeltaCon and Cut Distance, as well as methods not requiring a priori known node-correspondence, such as alignment-based, graphlet-based, and spectral methods, and the recently proposed Portrait Divergence and NetLSD. We test the above methods on synthetic networks and we assess their usability and the meaningfulness of the results they provide. Finally, we apply the methods to two real-world datasets, the European Air Transportation Network and the FAO Trade Network, in order to discuss the results that can be drawn from this type of analysis.