Towards real-world complexity: an introduction to multiplex networks

Many real-world complex systems are best modeled by multiplex networks of interacting network layers. The multiplex network study is one of the newest and hottest themes in the statistical physics of complex networks. Pioneering studies have proven that the multiplexity has broad impact on the system's structure and function. In this Colloquium paper, we present an organized review of the growing body of current literature on multiplex networks by categorizing existing studies broadly according to the type of layer coupling in the problem. Major recent advances in the field are surveyed and some outstanding open challenges and future perspectives will be proposed.Comment: 20 pages, 10 figure

Hierarchical sequencing of online social graphs

In online communications, patterns of conduct of individual actors and use of emotions in the process can lead to a complex social graph exhibiting multilayered structure and mesoscopic communities. Using simplicial complexes representation of graphs, we investigate in-depth topology of online social network which is based on MySpace dialogs. The network exhibits original community structure. In addition, we simulate emotion spreading in this network that enables to identify two emotion-propagating layers. The analysis resulting in three structure vectors quantifies the graph's architecture at different topology levels. Notably, structures emerging through shared links, triangles and tetrahedral faces, frequently occur and range from tree-like to maximal 5-cliques and their respective complexes. On the other hand, the structures which spread only negative or only positive emotion messages appear to have much simpler topology consisting of links and triangles. Furthermore, we introduce the node's structure vector which represents the number of simplices at each topology level in which the node resides. The total number of such simplices determines what we define as the node's topological dimension. The presented results suggest that the node's topological dimension provides a suitable measure of the social capital which measures the agent's ability to act as a broker in compact communities, the so called Simmelian brokerage. We also generalize the results to a wider class of computer-generated networks. Investigating components of the node's vector over network layers reveals that same nodes develop different socio-emotional relations and that the influential nodes build social capital by combining their connections in different layers.Comment: 17 pages, 19 figure

Anatomy and efficiency of urban multimodal mobility

International audienceThe growth of transportation networks and their increasing interconnections, although positive,has the downside effect of an increasing complexity which make them difficult to use, to assess, andlimits their efficiency. On average in the UK, 23% of travel time is lost in connections for trips withmore than one mode, and the lack of synchronization decreases very slowly with population size.This lack of synchronization between modes induces differences between the theoretical quickest tripand the ‘time-respecting’ path, which takes into account waiting times at interconnection nodes.We analyse here the statistics of these paths on the multilayer, temporal network of the entire,multimodal british public transportation system. We propose a statistical decomposition – the‘anatomy’ – of trips in urban areas, in terms of riding, waiting and walking times, and which showshow the temporal structure of trips varies with distance and allows us to compare different cities.Weaknesses in systems can be either insufficient transportation speed or service frequency, but thekey parameter controlling their global efficiency is the total number of stop events per hour for allmodes. This analysis suggests the need for better optimization strategies, adapted to short, longunimodal or multimodal trips

Dynamic processes on networks and higher-order structures

Higher-order interactions are increasingly recognized as a critical aspect in the modeling of complex systems. Higher-order networks provide a framework for studying the relationship between the structure of higher-order interactions and the function of the complex system. However, little is known about how higher-order interactions affect dynamic processes. In this thesis, we develop general frameworks of percolation aiming at understanding the interplay between higher-order network structures and the critical properties of dynamics. We reveal that degree correlations strongly affect the percolation threshold on higher-order networks and interestingly, the effect of correlations is different on ordinary percolation and higher-order percolation. We further elucidate the mechanisms responsible for the emergence of discontinuous transitions on higher-order networks. Moreover, we show that triadic regulatory interaction, as a general type of higher-order interaction found widely in nature, can turn percolation into a fully-fledged dynamic process that exhibits period doubling and a route to chaos. As an important example of dynamic processes, we further investigate the role of network topology on epidemic spreading. We show that higher-order interactions can induce a non-linear infection kernel in a pandemic, which results in a discontinuous phase transition, hysteresis, and superexponential spreading. Finally, we propose an epidemic model to evaluate the role of automated contact-and-tracing with mobile apps as a new containment measure to mitigate a pandemic. We reveal the non-linear effect on the reduction of the incidence provided by a certain fraction of app adoption in the population and we propose the optimal strategy to mitigate the pandemic with limited resources. Altogether, the thesis provides new insights into the interplay between the topology of higher-order networks and their dynamics. The results obtained may shed light on the research in other areas of interest such as brain functions and epidemic spreading

EUSN 2021 Book of Abstracts, Fifth European Conference on Social Networks

Book of abstract of the fifth European conference on Social Networks EUSN 202

Structure and dynamics of policy induced networks in systems of innovation

The granting of publicly subsidized joint projects has become a popular policy instrument in both Germany and the European Union. However, little is known about how the emerging subsidized network affects the allocation process of future project grants. Employing unique databases containing information about government funded R&D projects , this book analyzes the extent to which the funding network becomes shaped by a self-enforced project allocation mechanism . The empirical results show that participation within a collaborative project does not raise, per se, the chance of an organization obtaining another project grant. Rather, it is important to hold central positions within the network in order to increase the likelihood of receiving new subsidies

Statistical physics approaches to large-scale socio-economic networks

Die statistische Physik erforschte im letzten Jahrzehnt eine Fülle von wissenschaftlichen Gebieten, was zu einem besseren quantitativen Verständnis von verschiedenen, aus vielen Elementen bestehenden Systemen, z.B. von sozialen Systemen, geführt hat. Eine empirische Quantifizierung von menschlichem Verhalten auf gesellschaftlichem Niveau hat sich allerdings bisher als sehr schwierig erwiesen, wegen Problemen bei der Gewinnung und Qualität von Daten. In dieser Doktorarbeit erstellen wir zum ersten mal einen umfangreichen über fünf Jahre gesammelten Datensatz, der praktisch alle Aktionen und Eigenschaften der 350.000 Teilnehmer einer gesamten menschlichen Gesellschaft aus einem selbstentwickelten Massive Multiplayer Online Game enthält. Wir beschreiben dieses aus stark wechselwirkenden Spielern bestehende soziale System in drei Ebenen. In einem ersten Schritt analysieren wir die Individuen und deren Verhalten im Verlauf der Zeit. Eine Skalen- und Fluktuationsanalyse von Aktions-Reaktions-Zeitreihen enthüllt Persistenz der möglichen Aktionen und qualitative Unterschiede zwischen "guten" und "schlechten" Spielern. Wir untersuchen danach den Diffusionsprozess der im Spieluniversum stattfindenden Bewegungen der Individuen. Wir finden Subdiffusivität und eine durch ein Potenzgesetz verteilte Präferenz zu kürzlich besuchten Orten zurückzukehren. Zweitens, auf der nächsthöheren Ebene, verwenden wir Netzwerktheorie um die topologische Struktur der Interaktionen zwischen Individuen zu quantifizieren. Wir konzentrieren uns auf sechs durch direkte Interaktionen definierte Netzwerke, drei davon positiv (Handel, Freundschaft, Kommunikation), drei negativ (Feindschaft, Attacke, Bestrafung). Diese Netzwerke weisen nichttriviale statistische Eigenschaften auf, z.B. skaleninvariante Topologie, und entwickeln sich in der Zeit, was uns erlaubt eine Reihe von Hypothesen über sozialdynamische Phänomene zu testen. Wir finden qualitative Unterschiede zwischen positiven und negativen Netzwerken in Evolution und Struktur. Schließlich untersuchen wir das Multiplex-Netzwerk der Spielergesellschaft, das sich aus den einzelnen Netzwerk-Schichten zusammensetzt. Wir quantifizieren Interaktionen zwischen verschiedenen Netzwerken und zeigen die nichttrivialen Organisationsprinzipien auf die auch in echten menschlichen Gesellschaften beobachtet wurden. Unsere Erkenntnisse liefern Belege für die Hypothese der strukturellen Balance, die eine Vermeidung von gewissen frustrierten Zuständen auf mikroskopischem Niveau postuliert. Mit diesem Aufbau demonstrieren wir die Möglichkeit der Gewinnung neuartiger wissenschaftlicher Erkenntnisse über die Natur von kollektivem menschlichen Verhalten in großangelegten sozialen Systemen.In the past decade a variety of fields has been explored by statistical physicists, leading to an increase of our quantitative understanding of various systems composed of many interacting elements, such as social systems. However, an empirical quantification of human behavior on a societal level has so far proved to be tremendously difficult due to problems in data availability, quality and ways of acquisition. In this doctoral thesis we compile for the first time a large-scale data set consisting of practically all actions and properties of 350,000 odd participants of an entire human society interacting in a self-developed Massive Multiplayer Online Game, over a period of five years. We describe this social system composed of strongly interacting players in the game in three consecutive levels. In a first step, we examine the individuals and their behavioral properties over time. A scaling and fluctuation analysis of action-reaction time-series reveals persistence of the possible actions and qualitative differences between "good" and "bad" players. We then study and model the diffusion process of human mobility occurring within the "game universe". We find subdiffusion and a power-law distributed preference to return to more recently visited locations. Second, on a higher level, we use network theory to quantify the topological structure of interactions between the individuals. We focus on six network types defined by direct interactions, three of them with a positive connotation (trade, friendship, communication), three with a negative one (enmity, attack, punishment). These networks exhibit non-trivial statistical properties, e.g. scale-free topology, and evolve over time, allowing to test a series of long-standing social-dynamics hypotheses. We find qualitative differences in evolution and topological structure between positive and negative tie networks. Finally, on a yet higher level, we consider the multiplex network of the player society, constituted by the coupling of the single network layers. We quantify interactions between different networks and detect the non-trivial organizational principles which lead to the observed structure of the system and which have been observed in real human societies as well. Our findings with the multiplex framework provide evidence for the half-century old hypothesis of structural balance, where certain frustrated states on a microscopic level tend to be avoided. Within this setup we demonstrate the feasibility for generating novel scientific insights on the nature of collective human behavior in large-scale social systems