Network depth: identifying median and contours in complex networks

Centrality descriptors are widely used to rank nodes according to specific concept(s) of importance. Despite the large number of centrality measures available nowadays, it is still poorly understood how to identify the node which can be considered as the `centre' of a complex network. In fact, this problem corresponds to finding the median of a complex network. The median is a non-parametric and robust estimator of the location parameter of a probability distribution. In this work, we present the most natural generalisation of the concept of median to the realm of complex networks, discussing its advantages for defining the centre of the system and percentiles around that centre. To this aim, we introduce a new statistical data depth and we apply it to networks embedded in a geometric space induced by different metrics. The application of our framework to empirical networks allows us to identify median nodes which are socially or biologically relevant

Efficient network exploration by means of resetting self-avoiding random walkers

The self-avoiding random walk (SARW) is a stochastic process whose state variable avoids returning to previously visited states. This non-Markovian feature has turned SARWs a powerful tool for modelling a plethora of relevant aspects in network science, such as network navigability, robustness and resilience. We analytically characterize self-avoiding random walkers that evolve on complex networks and whose memory suffers stochastic resetting, that is, at each step, with a certain probability, they forget their previous trajectory and start free diffusion anew. Several out-of-equilibrium properties are addressed, such as the time-dependent position of the walker, the time-dependent degree distribution of the non-visited network and the first-passage time distribution, and its moments, to target nodes. We examine these metrics for different resetting parameters and network topologies, both synthetic and empirical, and find a good agreement with simulations in all cases. We also explore the role of resetting on network exploration and report a non-monotonic behavior of the cover time: frequent memory resets induce a global minimum in the cover time, significantly outperforming the well-known case of the pure random walk, while reset events that are too spaced apart become detrimental for the network discovery. Our results provide new insights into the profound interplay between topology and dynamics in complex networks, and shed light on the fundamental properties of SARWs in nontrivial environments.Comment: 10 pages & 3 figures; Supp. Mat.: 11 pages & 15 figure

Unraveling the hidden organisation of urban systems and their mobility flows

Increasing evidence suggests that cities are complex systems, with structural and dynamical features responsible for a broad spectrum of emerging phenomena. Here we use a unique data set of human flows and couple it with information on the underlying street network to study, simultaneously, the structural and functional organisation of 10 world megacities. We quantify the efficiency of flow exchange between areas of a city in terms of integration and segregation using well defined measures. Results reveal unexpected complex patterns that shed new light on urban organisation. Large cities tend to be more segregated and less integrated, while their overall topological organisation resembles that of small world networks. At the same time, the heterogeneity of flows distribution might act as a catalyst for further integrating a city. Our analysis unravels how human behaviour influences, and is influenced by, the urban environment, suggesting quantitative indicators to control integration and segregation of human flows that can be used, among others, for restriction policies to adopt during emergencies and, as an interesting byproduct, allows us to characterise functional (dis)similarities of different metropolitan areas, countries, and cultures.Comment: The first version on the arxiv is the extended version of the report presented to the Foursquare Future City Challenge 2019 https://www.futurecitieschallenge.com and presented at the NetMob19 Conference In Oxford. The second is the preprint of the published pape

Cities of a feather flock together: a study on the synchronization of communication between Italian cities

Abstract Due to the rise of communication technologies and economic globalization, modern large cities are becoming more and more interconnected and this phenomenon leads to an increasing synchronization in activities and communication patterns. In our work, we explore the communication synchronization between 76 Italian cities of different sizes by using mobile phone data. Our results show that both the spatial distance and the size of the city influence the synchronization: larger cities are more similar to larger cities in communication rhythms than medium cities are to medium cities, and medium cities are more similar to medium cities than smaller cities are to smaller cities. Furthermore, for all the cities' sizes we observe a drift in similarity due to spatial distance. Interestingly, the drift due to distance over similarity is less strong in large cities, that act as gateway nodes for the Italian economical system, hence having an emerging strongly connected and synchronized network, than for medium and small cities, that are more bounded to local industries. Finally, our results also show that highly synchronized cities are richer and more attractive for foreign-born population

Diffusion geometry of multiplex and interdependent systems

none2Complex networks are characterized by latent geometries induced by their topology or by the dynamics on them. In the latter case, different network-driven processes induce distinct geometric features that can be captured by adequate metrics. Random walks, a proxy for a broad spectrum of processes, from simple contagion to metastable synchronization and consensus, have been recently used, Domenico [Phys. Rev. Lett. 118, 168301 (2017)] to define the class of diffusion geometries and pinpoint the functional mesoscale organization of complex networks from a genuine geometric perspective. Here we first extend this class to families of distinct random walk dynamics—including local and nonlocal information—on multilayer networks—a paradigm for biological, neural, social, transportation, and financial systems—overcoming limitations such as the presence of isolated nodes and disconnected components, typical of real-world networks. We then characterize the multilayer diffusion geometry of synthetic and empirical systems, highlighting the role played by different random search dynamics in shaping the geometric features of the corresponding diffusion manifolds.noneGiulia Bertagnolli; Manlio De DomenicoBertagnolli, Giulia; De Domenico, Manli

Quantifying efficient information exchange in real network flows

While the global efficiency measures how easy it is to travel or exchange information concurrently between any two nodes in a network, this might be difficult to compute when networks are not embedded into space and edge weights do not encode physical distances, but instead represent flows. Here, the authors propose and analyse an efficiency measure based on the flow across least resistance pathways that can be computed without any knowledge on the system except for its weighted representation

CovMulNet19, Integrating Proteins, Diseases, Drugs, and Symptoms: A Network Medicine Approach to COVID-19

Introduction: We introduce in this study CovMulNet19, a comprehensive COVID-19 network containing all available known interactions involving SARS-CoV-2 proteins, interacting-human proteins, diseases and symptoms that are related to these human proteins, and compounds that can potentially target them. Materials and Methods: Extensive network analysis methods, based on a bootstrap approach, allow us to prioritize a list of diseases that display a high similarity to COVID-19 and a list of drugs that could potentially be beneficial to treat patients. As a key feature of CovMulNet19, the inclusion of symptoms allows a deeper characterization of the disease pathology, representing a useful proxy for COVID-19-related molecular processes. Results: We recapitulate many of the known symptoms of the disease and we find the most similar diseases to COVID-19 reflect conditions that are risk factors in patients. In particular, the comparison between CovMulNet19 and randomized networks recovers many of the known associated comorbidities that are important risk factors for COVID-19 patients, through identified similarities with intestinal, hepatic, and neurological diseases as well as with respiratory conditions, in line with reported comorbidities. Conclusion: CovMulNet19 can be suitably used for network medicine analysis, as a valuable tool for exploring drug repurposing while accounting for the intervening multidimensional factors, from molecular interactions to symptoms.Peer ReviewedPostprint (published version

Cities of a feather flock together: a study on the synchronization of communication between Italian cities

Due to the rise of communication technologies and economic globalization, modern large cities are becoming more and more interconnected and this phenomenon leads to an increasing synchronization in activities and communication patterns. In our work, we explore the communication synchronization between 76 Italian cities of different sizes by using mobile phone data. Our results show that both the spatial distance and the size of the city influence the synchronization: larger cities are more similar to larger cities in communication rhythms than medium cities are to medium cities, and medium cities are more similar to medium cities than smaller cities are to smaller cities. Furthermore, for all the cities’ sizes we observe a drift in similarity due to spatial distance. Interestingly, the drift due to distance over similarity is less strong in large cities, that act as gateway nodes for the Italian economical system, hence having an emerging strongly connected and synchronized network, than for medium and small cities, that are more bounded to local industries. Finally, our results also show that highly synchronized cities are richer and more attractive for foreign-born population

Multilayer Network Science

Networks are convenient mathematical models to represent the structure of complex systems, from cells to societies. In the last decade, multilayer network science – the branch of the field dealing with units interacting in multiple distinct ways, simultaneously – was demonstrated to be an effective modeling and analytical framework for a wide spectrum of empirical systems, from biopolymers networks (such as interactome and metabolomes) to neuronal networks (such as connectomes), from social networks to urban and transportation networks. In this Element, a decade after one of the most seminal papers on this topic, the authors review the most salient features of multilayer network science, covering both theoretical aspects and direct applications to real-world coupled/interdependent systems, from the point of view of multilayer structure, dynamics and function. The authors discuss potential frontiers for this topic and the corresponding challenges in the field for the next future

Acute electrocardiographic differences between Takotsubo cardiomyopathy and anterior ST elevation myocardial infarction

Background The aim of this study was to compare ECG findings between anterior ST elevation myocardial infarction (STEMI) and Takotsubo cardiomyopathy (TC) in a similar sample of postmenopausal women. Methods Between 2008 and 2011, 27 patients with TC were retrospectively enrolled and matched with 27 STEMI patients with the same age and sex taken from the prospective database of our laboratory. Results The absence of abnormal Q waves, the ST depression in aVR and the lack of ST elevation in V1 were significantly associated with TC (respectively: 52% vs 18%, p = 0.01; 47% vs 11%, p = 0.01; 80% vs 41%, p = 0.01). The combination of these ECG findings identified TC with a specificity of 95% and a positive predictive value of 85.7%. Conclusions The ECG on admission may be useful to distinguish TC from anterior STEMI. The combination of three ECG findings identifies patients with TC with high specificity and positive predictive value