Session J54: Focus Session: Complex and Co-evolving Networks - Empirical Studies of Social Networks

Modeling users' activity on Twitter networks: validation of Dunbar's number

Microblogging and mobile devices appear to augment human social capabilities, which raises the question whether they remove cognitive or biological constraints on human communication. In this paper we analyze a dataset of Twitter conversations collected across six months involving 1.7 million individuals and test the theoretical cognitive limit on the number of stable social relationships known as Dunbar's number. We find that the data are in agreement with Dunbar's result; users can entertain a maximum of 100-200 stable relationships. Thus, the ``economy of attention'' is limited in the online world by cognitive and biological constraints as predicted by Dunbar's theory. We propose a simple model for users' behavior that includes finite priority queuing and time resources that reproduces the observed social behavior.   

Entropy of dynamical social networks

Dynamical social networks are evolving rapidly and are highly adaptive. Characterizing the information encoded in social networks is essential to gain insight into the structure, evolution, adaptability and dynamics. Recently entropy measures have been used to quantify the information in email correspondence, static networks and mobility patterns. Nevertheless, we still lack methods to quantify the information encoded in time-varying dynamical social networks. In this talk we present a model to quantify the entropy of dynamical social networks and use this model to analyze the data of phone-call communication. We show evidence that the entropy of the phone-call interaction network changes according to circadian rhythms. Moreover we show that social networks are extremely adaptive and are modified by the use of technologies such as mobile phone communication. Indeed the statistics of duration of phone-call is described by a Weibull distribution and is significantly different from the distribution of duration of face-to-face interactions in a conference. Finally we investigate how much the entropy of dynamical social networks changes in realistic models of phone-call or face-to face interactions characterizing in this way different type human social behavior.   

The nature and perception of fluctuations in human musical rhythms

Although human musical performances represent one of the most valuable achievements of mankind, the best musicians perform imperfectly. Musical rhythms are not entirely accurate and thus inevitably deviate from the ideal beat pattern. Nevertheless, computer generated perfect beat patterns are frequently devalued by listeners due to a perceived lack of human touch. Professional audio editing software therefore offers a humanizing feature which artificially generates rhythmic fluctuations. However, the built-in humanizing units are essentially random number generators producing only simple uncorrelated fluctuations. Here, for the first time, we establish long-range fluctuations as an inevitable natural companion of both simple and complex human rhythmic performances [1]. Moreover, we demonstrate that listeners strongly prefer long-range correlated fluctuations in musical rhythms. Thus, the favorable fluctuation type for humanizing interbeat intervals coincides with the one generically inherent in human musical performances. [1] HH et al., PLoS ONE,6,e26457 (2011)   

Structural and social aspects of human mobility

Research on human mobility has been revolutionized by cellular phone data, capturing activity patterns across extensive populations. A number of interesting features have been discovered, including the ultra-slow growth of human mobility patterns, which cannot be reproduced by traditional random-walk models. However, the spatiotemporal flows and detailed microstructure of human mobility have not been well studied. Inferring complex mobility networks from country-wide data from mobile phone data, we find that human mobility is dominated by a small group of frequently visited and dynamically close locations, forming a primary ``habitat'' that captures typical behavior, along with subsidiary habitats representing additional travel. These habitats are both well separated and spatially compact. We find that motion within habitats exhibits distinct temporal scaling and that the time delay to enter subsidiary habitats is a primary factor in the spatiotemporal growth of human travel. Mobility is also coupled with social activity. Interestingly, many phone users possess habitats that occupy single temporal and social contexts and display high temporal and social predictability when occupying subsidiary habitats, revealing new connections between human activity and mobility dynamics.   

Temporal and spatial regularity of mobile-phone data

Network science is a vibrant, interdisciplinary research area with strong connections to a plethora of different fields. As the amount of empirically obtained datasets increases more and more, approaches from network sciences continue to enhance our understanding, for instance, of human dynamics. The available data often consist of temporal as well as spatial information. In our case they originate from anonymized mobile-phone traces, which include information about the timing of the connections between two mobile phones and also their positions. Thus, the data contains an additional social component. In this study, we evaluate patterns of human behavior identifying both temporal and spatial regularity. This leads to a detailed mobility analysis on various timescales and contributes to a general theory of synchronization in complex, real-world networks.   

Scale-free correlations in the geographical spreading of obesity

Obesity levels have been universally increasing. A crucial problem is to determine the influence of global and local drivers behind the obesity epidemic, to properly guide effective policies. Despite the numerous factors that affect the obesity evolution, we show a remarkable regularity expressed in a predictable pattern of spatial long-range correlations in the geographical spreading of obesity. We study the spatial clustering of obesity and a number of related health and economic indicators, and we use statistical physics methods to characterize the growth of the resulting clusters. The resulting scaling exponents allow us to broadly classify these indicators into two separate universality classes, weakly or strongly correlated. Weak correlations are found in generic human activity such as population distribution and the growth of the whole economy. Strong correlations are recovered, among others, for obesity, diabetes, and the food industry sectors associated with food consumption. Obesity turns out to be a global problem where local details are of little importance. The long-range correlations suggest influence that extends to large scales, hinting that the physical model of obesity clustering can be mapped to a long-range correlated percolation process.   

Mining networks of human contact with wearable sensors

Due to the development of sensors of various types and the use of digital media and computational devices, we increasingly leave digital traces of our daily activities. The scale at which such data can be gathered and analyzed makes possible a novel, data-driven approach to the investigation of various aspects of human behavior. In this talk, I will focus on the research done within the SocioPatterns project (www.sociopatterns.org), in which we have developed the SocioPatterns sensing platform to obtain longitudinal datasets on face-to-face contact events between individuals in a variety of contexts ranging from scientific conferences to museum, schools or hospitals. The gathered data sets consists in dynamic networks of human contacts, and their analysis reveal interesting similarities and differences of human interaction patterns across contexts. I will also consider the impact of the temporal resolution, which allows to take into account causality constraints, on dynamical processes occurring on networks, such as spreading processes.   

Are we in our travel decisions self-determined?

Mobile phone data, as saved by every phone provider worldwide, allows us to extract information about human mobility. It can be mainly used to study the locations and routes of each mobile phone user during entire months. In order to gain deeper understanding of the inherent travel decisions of the daily trips measured by phone data, we compare them statically with those extracted from 10,000 trajectories reported in a travel diary survey. We identify and compare from both data sets the underlying trip decisions networks or motifs. Interestingly, although millions of different motifs are possible, in both data sets we found similar motif distributions. Hence, we develop a simple model, which could reproduce not only the size distribution of the motifs, but the motifs themselves and answer the opening question.   

A cross-section test of Cobb-Douglass production function between market capitalization and GDP

Most classical economic theories imply that both (a) economies with lower output (GDP) per person tend to grow faster in per capita terms and (b) economies with lower capital per person tend to grow faster in per capita terms. It is well-known that the former was found to be wrong. Taking market capitalization as a proxy for physical capital, we analyze a cohort of countries over a 17-year period (1994-2010) and we find the latter statement in agreement with empirical data implying a contradictive result that while capital data worldwide tend to converge, GDP data tend to diverge. However, for the countries analyzed, for which we have both market capitalization and GDP data, we find that even economies with lower output (GDP) per person tend to grow faster in per capita terms. The result that for all countries one obtains divergence while for a group of countries having both market capitalization and GDP data we have convergence is in contrast with the refutation of (a) but our results only apply to countries that have an exchange market, and are thus participating in globalization, indicating the convergent effect of globalization.   

Statistical Analysis on the Korean Transportation System

We investigate the Korean transportation system including subway, highway and express bus systems. The network topology and traffic pattern of the Korean transportation system is studied. We find the transportation have many complexity features such as scale-free property. We also find the relationship between the traffic flow, and the population and the distance.   

The Growth Dynamics of Words: How Historical Context Shapes the Competitive Linguistic Environment

Using the massive Google n-gram database of over 10$^{11}$ word uses in English, Hebrew, and Spanish, we explore the connection between the growth rates of relative word use and the observed growth rates of disparate competing actors in a common environment such as businesses, scientific journals, and universities, supporting the concept that a language's lexicon is a generic arena for competition, evolving according to selection laws. We find aggregate-level anomalies in the collective statistics corresponding to the time of key historical events such as World War II and the Balfour Declaration.   

Voronoi Cell Patterns: Application of the size distribution to societal systems

In studying the growth of islands on a surface subjected to a particle flux, we found it useful to characterize the distribution of the areas of associated Voronoi (proximity or Wigner-Seitz) cells in terms of the generalized Wigner surmise\footnote{AP \& TLE, PRL 99 (2007) 226102; PRL 104 (2010) 149602} and the gamma distributions. Here we show that the same concepts and distributions are useful in analyzing several problems arising in society.\footnote{DLG et al., arXiv 1109.3994; RS, Ph.D. dissertation; RS et al., preprint} We analyze the 1D problem of the distribution of gaps between parked cars, assuming that successive cars park in the middle of vacant spaces, and compare with published data. We study the formation of second-level administrative divisions, e.g. French {\it arrondissements}. We study the actual distribution of {\it arrondissements} and the Voronoi tessellation associated with the chief town in each. While generally applicable, there are subtleties in some cases. Lastly, we consider the pattern formed by Paris M\'etro stations and show that near the central area, the associated Voronoi construction also has this sort of distribution.