Emergence of encounter networks due to human mobility

RESEARCH ARTICLE Emergence of encounter networks due to human mobility A. P. Riascos1☯*, José L. Mateos2☯ 1 Department of Civil Engineering, Universidad Mariana, San Juan de Pasto, Colombia, 2 Instituto de Fı́sica, Universidad Nacional Autónoma de México, Ciudad de México, México ☯ These authors contributed equally to this work. * a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 OPEN ACCESS Citation: Riascos AP, Mateos JL (2017) Emergence of encounter networks due to human mobility. PLoS ONE 12(10): e0184532. https://doi. org/10.1371/journal.pone.0184532 Editor: Wei-Xing Zhou, East China University of Science and Technology, CHINA Received: May 4, 2017 Accepted: August 25, 2017 Abstract There is a burst of work on human mobility and encounter networks. However, the connection between these two important fields just begun recently. It is clear that both are closely related: Mobility generates encounters, and these encounters might give rise to contagion phenomena or even friendship. We model a set of random walkers that visit locations in space following a strategy akin to Lévy flights. We measure the encounters in space and time and establish a link between walkers after they coincide several times. This generates a temporal network that is characterized by global quantities. We compare this dynamics with real data for two cities: New York City and Tokyo. We use data from the location-based social network Foursquare and obtain the emergent temporal encounter network, for these two cities, that we compare with our model. We found long-range (Lévy-like) distributions for traveled distances and time intervals that characterize the emergent social network due to human mobility. Studying this connection is important for several fields like epidemics, social influence, voting, contagion models, behavioral adoption and diffusion of ideas. Published: October 12, 2017 Copyright: © 2017 Riascos, Mateos. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: All relevant data are within the paper and its Supporting Information files. Funding: A.P.R. acknowledges support from the Secretarı́a de Ciencia, Tecnologı́a e Innovación (SECITI), the Centro Latinoamericano de Fı́sica (CLAF), and the Consejo Nacional de Ciencia y Tecnologı́a (CONACYT), México: The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing interests: The authors have declared that no competing interests exist. Introduction There is a burst of studies on human mobility nowadays due to the increasing availability of data that allow us to determine, using mobile phones and location-based social networks, the spatial location of people. On the other hand, it is clear that there must be an intimate connection between human mobility and encounter networks. People tend frequently to visit popular places in a city meeting other people there. If this occurs often, there is a chance that a contagion process takes place. In this way, there is feedback between human mobility in space and the structure of the encounter network. The goal of this research is to study the emergence of encounter networks due to human mobility in cities. The science of networks has witness an exponential growth due to the ubiquity of the concept of network in many areas of the human endeavor [1]. In particular, social networks are now studied not only by researchers on the social sciences, but by people on the exact sciences as well [2]. All this emergent science acquires importance due to the vast range of applications in many different areas. On the other hand, human mobility just recently started to be PLOS ONE | https://doi.org/10.1371/journal.pone.0184532 October 12, 2017 1 / 22 Encounter networks due to human mobility explored in detail, thanks to geolocalized data of mobile phones and location-based social networks. Some of these studies show that human mobility follows a long-range dynamics, akin to Lévy walks [3, 4], as has been shown before as a common strategy in many animal species and humans [5–14]. It is clear that the spatial effects imposed by cities affects the mobility patterns of humans by constraining the motion of individuals and providing efficient transportation networks that allows long-range displacements. Understanding human mobility in urban areas is an important and challenging problem due to the fact that millions of people live and interact in big cities [15]. The recent advent of diverse technologies that we use in our daily routines, like mobile phones and GPS, allows the study of urban human mobility in detail [10, 11, 16–22], with many applications in different multidisciplinary fields like epidemic spreading and contagion processes [23–26], social influence [27] and urban traffic [28, 29]. Recently the connection between social networks and mobility has started to be explored as well [30–38]. In this paper, we explore the emergence of encounter networks due to human mobility in cities. There are many different motivations of why people move. Of course, we live in specific locations and we have to move to work on a daily basis during the week. We need to move to many other places like banks, shops, markets, bars, restaurants, visit friends and so on. The studies of human mobility started to flourish due to the digital trace leave by mobile devices and the interaction of people through location-based social networks [18, 19, 21, 22, 29, 39– 45]. Some studies have addressed this type of mobility to characterize displacements of people from one location to another [46, 47], to identify patterns and routines in visited locations [18, 42, 48] and to establish statistical properties of the structure of spatial networks that emerge from the interplay between the locations in urban regions and human mobility [44, 49]. In addition to the spatial mobility and its structure, there are different types of networks associated with the interactions between humans; many of them coupled with spatial translations and inducing a collective dynamics. For example, many of our activities require to coincide spatially and temporally with people at work, in restaurants, in a party, in a train station, among many other places. Now, whereas different types of networks, in particular social networks, have been studied extensively in the last two decades, the way of how the social networks influence human mobility, and vice versa, has been explored only in recent times. The interplay between social networks and mobility has been explored in the context of contact networks [24, 33, 50–54], location based social networks [31, 55], face to face networks [56] and the spreading of diseases [23, 57–60]. Here, we analyze the dynamic (...truncated)