Densification and sparsification of temporal networks are attributed to two fundamental mechanisms: a change in the population in the system and/or a change in the chances that nodes in the system are connected. In theory, each of these mechanisms generates a distinctive type of densification scaling, but in reality both types are generally mixed. Here, we develop a Bayesian statistical method to identify the extent to which each of these mechanisms is at play at a given point in time, taking the mixed densification scaling as input. We apply the method to networks of face-to-face interactions of individuals and reveal that the main mechanism that causes densification and sparsification occasionally switches, the frequency of which depending on the social context. The proposed method uncovers an inherent regime-switching property of network dynamics, which will provide a new insight into the mechanics behind evolving social interactions.
Online multiplayer games are a popular form of social interaction, used by hundreds of millions of individuals. However, little is known about the social networks within these online games, or how they evolve over time. Understanding human social dynamics within massive online games can shed new light on social interactions in general and inform the development of more engaging systems. Here, we study a novel, large friendship network, inferred from nearly 18 billion social interactions over 44 weeks between 17 million individuals in the popular online game Halo: Reach. This network is one of …
Temporal social networks of human interactions are preponderant in understanding the fundamental patterns of human behavior. In these networks, interactions occur locally between individuals (i.e., nodes) who connect with each other at different times, culminating into a complex system-wide web that has a dynamic composition. Dynamic behavior in networks occurs not only locally but also at the global level, as systems expand or shrink due either to: changes in the size of node population or variations in the chance of a connection between two nodes. Here, we propose a numerical maximum-likelih…
Many real-world social networks constantly change their global properties over time, such as the number of edges, size and density. While temporal and local properties of social networks have been extensively studied, the origin of their dynamical nature is not yet well understood. Networks may grow or shrink if a) the total population of nodes changes and/or b) the chance of two nodes being connected varies over time. Here, we develop a method that allows us to classify the source of time-varying nature of temporal networks. In doing so, we first show empirical evidence that real-world dynami…
In this paper, we propose a new graph sampling method for online social networks that achieves the following. First, a sample graph should reflect the ratio between the number of nodes and the number of edges of the original graph. Second, a sample graph should reflect the topology of the original graph. Third, sample graphs should be consistent with each other when they are sampled from the same original graph. The proposed method employs two techniques: hierarchical community extraction and densification power law. The proposed method partitions the original graph into a set of communities t…
We present a deterministic model for on-line social networks (OSNs) based on transitivity and local knowledge in social interactions. In the Iterated Local Transitivity (ILT) model, at each time-step and for every existing node $x$, a new node appears which joins to the closed neighbour set of $x.$ The ILT model provably satisfies a number of both local and global properties that were observed in OSNs and other real-world complex networks, such as a densification power law, decreasing average distance, and higher clustering than in random graphs with the same average degree. Experimental studi…
We study the behaviour of a Schelling-class system in which a fraction $f$ of spatially-fixed switching agents is introduced. This new model allows for multiple interpretations, including: (i) random, non-preferential allocation (\textit{e.g.} by housing associations) of given, fixed sites in an open residential system, and (ii) superimposition of social and spatial mobility in a closed residential system.\\ We find that the presence of switching agents in a segregative Schelling-type dynamics can lead to the emergence of intermediate patterns (\textit{e.g.} mixture of patches, fuzzy interface…
Discontinuous phase transitions occurs to be particularly interesting from a social point of view because of their relationship to social hysteresis and critical mass. In this paper, we show that the replacement of a time-varying (annealed, situation-based) disorder by a static (quenched, personality-based) one can lead to a change from a continuous to a discontinuous phase transition. This is a result beyond the state of art, because so far numerous studies on various complex systems (physical, biological and social) have indicated that the quenched disorder can round or destroy the existence…
Quantification of human group-behavior has so far defied an empirical, falsifiable approach. This is due to tremendous difficulties in data acquisition of social systems. Massive multiplayer online games (MMOG) provide a fascinating new way of observing hundreds of thousands of simultaneously socially interacting individuals engaged in virtual economic activities. We have compiled a data set consisting of practically all actions of all players over a period of three years from a MMOG played by 300,000 people. This large-scale data set of a socio-economic unit contains all social and economic d…
Walking is a fundamental activity of our daily life not only for moving to other places but also for interacting with surrounding environment. While walking on the streets, pedestrians can be aware of attractions like shopping windows. They can be influenced by the attractions and some of them might shift their attention towards the attractions, namely switching behavior. As a first step to incorporate the switching behavior, this study investigates collective effects of switching behavior for an attraction by developing a behavioral model. Numerical simulations exhibit different patterns of p…
In this paper we study how the network of agents adopting a particular technology relates to the structure of the underlying network over which the technology adoption spreads. We develop a model and show that the network of agents adopting a particular technology may have characteristics that differ significantly from the social network of agents over which the technology spreads. For example, the network induced by a cascade may have a heavy-tailed degree distribution even if the original network does not. This provides evidence that online social networks created by technology adoption over…
This paper considers social learning amongst rational agents (for example, sensors in a network). We consider three models of social learning in increasing order of sophistication. In the first model, based on its private observation of a noisy underlying state process, each agent selfishly optimizes its local utility and broadcasts its action. This protocol leads to a herding behavior where the agents eventually choose the same action irrespective of their observations. We then formulate a second more general model where each agent is benevolent and chooses its sensor-mode to optimize a socia…
We study a model of information spreading on multiplex networks, in which agents interact through multiple interaction channels (layers), say online vs.\ offline communication layers, subject to layer-switching cost for transmissions across different interaction layers. The model is characterized by the layer-wise path-dependent transmissibility over a contact, that is dynamically determined dependently on both incoming and outgoing transmission layers. We formulate an analytical framework to deal with such path-dependent transmissibility and demonstrate the nontrivial interplay between the mu…
Punishment and partner switching are two well-studied mechanisms that support the evolution of cooperation. Observation of human behaviour suggests that the extent to which punishment is adopted depends on the usage of alternative mechanisms, including partner switching. In this study, we investigate the combined effect of punishment and partner switching in evolutionary prisoner's dilemma games conducted on a network. In the model, agents are located on the network and participate in the prisoner's dilemma games with punishment. In addition, they can opportunistically switch interaction partn…
Long-range social pressure and the evolution of cooperation in multiplex networks
Universidad Politécnica de Madrid（马德里理工大学）；Grupo de Investigación Ingeniería de Organización y Logística (IOL), Departamento de Ingeniería de Organización, Administración de Empresas y Estadística, Escuela Técnica Superior de Ingenieros Industriales, Universidad Politécnica de Madrid（马德里理工大学工业工程师高等学院组织工程、企业管理与统计学系组织工程与物流研究组（IOL））；Grupo Interdisciplinar de Sistemas Complejos (GISC)（复杂系统跨学科研究组（GISC））
Social distancing strategies have been adopted by governments to manage the COVID-19 pandemic, since the first outbreak began. However, further epidemic waves keep out the return of economic and social activities to their standard levels of intensity. Social distancing interventions based on control theory are needed to consider a formal dynamic characterization of the implemented SIR-type model to avoid unrealistic objectives and prevent further outbreaks. The objective of this work is twofold: to fully understand some dynamical aspects of SIR-type models under control actions (associated wit…
Multi-layered networks represent a major advance in the description of natural complex systems, and their study has shed light on new physical phenomena. Despite its importance, however, the role of the temporal dimension in their structure and function has not been investigated in much detail so far. Here we study the temporal correlations between layers exhibited by real social multiplex networks. At a basic level, the presence of such correlations implies a certain degree of predictability in the contact pattern, as we quantify by an extension of the entropy and mutual information analyses …
We analyze Axelrod's model of social interactions on coevolving complex networks. We introduce four extensions with different mechanisms of edge rewiring. The models are intended to catch two kinds of interactions - preferential attachment, which can be observed in scientists or actors collaborations, and local rewiring, which can be observed in friendship formation in everyday relations. Numerical simulations show that proposed dynamics can lead to the power-law distribution of nodes' degree and high value of the clustering coefficient, while still retaining the small-world effect in three mo…
The structure of social relations is fundamental for the construction of plausible simulation scenarios. It shapes the way actors interact and create their identity within overlapping social contexts. Each actor interacts in multiple contexts within different types of social relations that constitute their social space. In this article, we present an approach to model structured agent societies with multiple coexisting social networks. We study the notion of context permeability, using a game in which agents try to achieve global consensus. We design and analyse two different models of permeab…
DynamiX: Large-Scale Dynamic Social Network Simulator
School of Information Science and Technology, University of Science and Technology of China（信息科学与技术学院，中国科学技术大学）；Department of Computer Science, University of Rochester（计算机科学系，罗切斯特大学）
In recent years, there has been growing interest in the study of coevolutionary games on networks. Despite much progress, little attention has been paid to spatially embedded networks, where the underlying geographic distance, rather than the graph distance, is an important and relevant aspect of the partner rewiring process. It thus remains largely unclear how individual partner rewiring range preference, local vs. global, emerges and affects cooperation. Here we explicitly address this issue using a coevolutionary model of cooperation and partner rewiring range preference in spatially embedd…
Mobility is undergoing dramatic transformations. Especially in the context of urban areas, several significant changes are underway, driven by both new mobility needs and environmental concerns. The most mature one, which still is struggling to affirm itself is the process of the adoption of Electric Vehicles (EVs), thus switching from fuel-based to battery-powered propulsion technologies. Many social and economic barriers have proved to play a crucial role in this process, ranging from level of education, environmental awareness, age and census. This work aims at contributing to the study of …
COVID-19 abatement strategies have risks and uncertainties which could lead to repeating waves of infection. We show -- as proof of concept grounded on rigorous mathematical evidence -- that periodic, high-frequency alternation of into, and out-of, lockdown effectively mitigates second-wave effects, while allowing continued, albeit reduced, economic activity. Periodicity confers (i) predictability, which is essential for economic sustainability, and (ii) robustness, since lockdown periods are not activated by uncertain measurements over short time scales. In turn -- while not eliminating the v…
Public opinion is often affected by the presence of committed groups of individuals dedicated to competing points of view. Using a model of pairwise social influence, we study how the presence of such groups within social networks affects the outcome and the speed of evolution of the overall opinion on the network. Earlier work indicated that a single committed group within a dense social network can cause the entire network to quickly adopt the group's opinion (in times scaling logarithmically with the network size), so long as the committed group constitutes more than about 10% of the popula…
There is little doubt about whether social networks play a role in modern protests. This agreement has triggered an entire research avenue, in which social structure and content analysis have been central --but are typically exploited separately. Here, we combine these two approaches to shed light on the opinion evolution dynamics in Egypt during the summer of 2013 along two axes (Islamist/Secularist, pro/anti-military intervention). We intend to find traces of opinion changes in Egypt's population, paralleling those in the international community --which oscillated from sympathetic to condemn…
