Limited communication capacity unveils strategies for human interaction

Limited communication capacity unveils strategies for human interaction SUBJECT AREAS: SCIENTIFIC DATA COMPLEX NETWORKS APPLIED MATHEMATICS STATISTICAL PHYSICS Received 15 January 2013 Accepted 2 May 2013 Published 6 June 2013 Correspondence and requests for materials should be addressed to E.M. (emoro@math. uc3m.es) Giovanna Miritello1,2, Rubén Lara2, Manuel Cebrian3,4 & Esteban Moro1,5 1 Departamento de Matemáticas & GISC, Universidad Carlos III de Madrid, 28911 Leganés, Spain, 2Telefónica Research, 28050 Madrid, Spain, 3NICTA, Melbourne, Victoria 3010, Australia, 4Department of Computer Science & Engineering, University of California at San Diego, La Jolla, CA 92093, USA, 5Instituto de Ingenierı́a del Conocimiento, Universidad Autónoma de Madrid, 28049 Madrid, Spain. Connectivity is the key process that characterizes the structural and functional properties of social networks. However, the bursty activity of dyadic interactions may hinder the discrimination of inactive ties from large interevent times in active ones. We develop a principled method to detect tie de-activation and apply it to a large longitudinal, cross-sectional communication dataset (<19 months, <20 million people). Contrary to the perception of ever-growing connectivity, we observe that individuals exhibit a finite communication capacity, which limits the number of ties they can maintain active in time. On average men display higher capacity than women, and this capacity decreases for both genders over their lifespan. Separating communication capacity from activity reveals a diverse range of tie activation strategies, from stable to exploratory. This allows us to draw novel relationships between individual strategies for human interaction and the evolution of social networks at global scale. M any different forces govern the evolution of social relationships making them far from random. In recent years, the understanding of what mechanisms control the dynamics of activating or deactivating social ties have uncovered forces ranging from geography to structural positions in the social network (e.g. preferential attachment, triadic closure), to homophily1. These finding are pervasive in empirical analyses across cultures, communication technologies and interaction environments2–11. However, the incorrect assumption that time, attention and cognition are elastic resources has blurred the study of how individuals manage their social interactions over time12–14. Understanding such social strategies is not only of paramount importance to make progress in the characterization of human behavior, but also to improve our current description of social networks as evolutionary objects against the (aggregated) ever-growing or static pictures of the social structure. Several reasons have hampered the observation of tie activation/deactivation dynamics in social networks at large scale: on the one hand, studies of diffusion based on datasets from pre-electronic eras have safely assumed that tie activation/deactivation is a much slower process than interactions within a tie, and thus their dynamics might be safely neglected15–17. However, the current ability to communicate faster and further than ever accelerates tie dynamics in an unprecedented manner to the point that tie activation/deactivation may rival in time with processes like information spreading. On the other hand, available data about how ties form or decay were restricted to egocentric, small social networks and/or short periods of time which made it difficult to assess the universality of the results obtained and their extension to other situations5. Finally, although in some online social networks there are explicit rules for the establishment of social ties, in most cases activity is the only way to assess the existence of the tie18,19. Online social networks are plagued with this problem due to the cheap cost of maintaining ‘‘friends’’ which are in fact already deactivated relationships20. However, using activity as proxy for tie presence is a problem in most communication channels like mobile phone calls, emails, electronic social networks etc., since tie activity is very bursty21 and so far there is no clear method to discriminate those social ties that are already inactive from large-inter even times within active relationships42. Results Detection of tie activation/deactivation. To study the formation and decay of communication ties, we study the Call Detail Records (CDRs) from a single mobile phone operator over a period of 19 months. The data consists of the anonymized voice calls of about 20 million users that form 700 million communication ties. After filtering out all the incoming or outgoing calls that involve other operators, we only consider users that are active across the whole time period and retain only ties which are reciprocated. We refer to Methods Section and the Supplementary SCIENTIFIC REPORTS | 3 : 1950 | DOI: 10.1038/srep01950 1 www.nature.com/scientificreports Figure 1 | Detection of tie activation/deactivation. Schematic view of the time intervals considered in our database and the different situations of tie activation/deactivation and the interplay between the tie communication patterns and tie activation/deactivation for a given observation time window V of length T 5 7 months (shadowed area). Each line refers to a different tie while each vertical segment indicates a communication event between i « j and dtij is the inter-event time in the i « j time series. Information (SI) Section 7 for further details about the processing and the sampling of the datasets and for the comparison with another (smaller) database of Facebook communication through wall posts. In most studies of communication networks a tie is assumed to be present if it shows any activity in the observation window22. However, since communication is bursty21, large inter-event times between interactions are likely and thus they might be unobserved or mistaken as tie decay or formation, specially if the observation window is short (see Fig. 1 and SI Section 1). For example, in our call database we find that the average time between tie communication events is Ædtijæ 5 14 days (with s 5 18 days) and thus we might get spurious effects if the observation window is of the order of months, as repeated interactions may fall outside the observation window23. To overcome this we propose a different method to assess whether a tie has been activated/deactivated in the observation window V. The method is based on the observation of tie activity in a time window before/after V: if tie activity is observed in the 6 months before V then it is considered an old tie [cases (a) and (d) in Fig. 1]; on the other hand, if activity is observed in the 6 months after V we will assume that the tie persists [cases (b) and (d) in Fig. 1]. In any other case, we will consider that the tie is activated and/or deactivated in V [cases (a), (b) and (c) in Fig. 1]. Of co (...truncated)