Statistical Properties of Social Group Evolution

Statistical Properties of Social Group Evolution

Gergely Palla (Statistical and Biological Research Group of the Hungarian Academy of Sciences, Hungary) and Tamás Vicsek (Statistical and Biological Research Group of the Hungarian Academy of Sciences, Hungary & Eötvös University, Hungary)
DOI: 10.4018/978-1-60960-171-3.ch003
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Abstract

The authors’ focus is on the general statistical features of the time evolution of communities (also called as modules, clusters or cohesive groups) in large social networks. These structural sub-units can correspond to highly connected circles of friends, families, or professional cliques, which are subject to constant change due to the intense fluctuations in the activity and communication patterns of people. The communities can grow by recruiting new members, or contract by loosing members; two (or more) groups may merge into a single community, while a large enough social group can split into several smaller ones; new communities are born and old ones may disappear. According to our results, the time evolution of social groups containing only a few members and larger communities, e.g., institutions show significant differences.
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Introduction

Until the recent past, social network research was based on questionnaire data, reaching typically a few dozen individuals (Granovetter, 1992; Wasserman, 1994; White, 1976). The main advantage of this approach is that it can provide very detailed information concerning the ties between people: what sort of acquaintance is it based on, how intense is the relation, whether it is mutual or not, what is the emotional background behind the connection, etc. However, a major drawback is that the size of the sample that can be generated this way is very limited, and as long as it is based solely on the opinion of the surveyed people, the strength of the ties remains subjective.

A major shift in paradigm begun to take place in this field around the millennium, when large datasets describing various social relations between people have become available for research (Barabási, 2003; Mendes & Dorogovtsev, 2003; Watts & Strogatz, 1998). Due to the rapid development in informatics, the handling of social networks constructed from e-mail or phone-call records with more than a million nodes can be easily solved with present day computers. When compared to the questionnaire date, the information about the individual links is limited in these systems. However, the strength of the ties can be measured in more objective way, by e.g., aggregating the number of e-mails or phone-calls between the people. One of the first results obtained from the analysis of large scale social networks based on automated data collection was given by Onnela et al. (2007), providing empirical evidence for the famous Granovetter hypothesis (Granovetter, 1973) in a mobile phone network. Due to the richness of mobile phone data a series of other important studies followed along this line, dealing with problems spreading from human mobility patterns (González, Hidalgo & Barabási, 2008), through the laws of geographical dispersal of social connections (Lambiotte, Blondel, de Kerchove, Huens, Prieur, Smoreda & Van Dooren, 2008) to the spread of mobile phone viruses (Wang, González, Hidalgo & Barabási, 2009). Along with intense research of mobile phone networks, the field of complex network proliferated in other directions as well. The recently opened frontiers in this multidisciplinary area include the study of tagged networks (Cattuto, Loreto & Pietronero, 2007; Cattuto, Barrat, Baldassarri, Schehrd &Loreto, 2009; Palla, Farkas, Pollner, Derényi & Vicsek, 2008) and hyper-graphs (Zlatic, Ghoshal &Caldarelli, 2009; Ghoshal, Zlatic, Caldarelli & Newman, 2009), and the development of general network models, capable of producing random graphs with diverse properties (Leskovec, Chakrabarti, Kleinberg & Faloutsos, 2005; Mahadevan, Krioukov, Fall &Vahdat, 2006; Robins, Snijders, Wang, Handcock & Pattison, 2007; Palla, Lovász & Vicsek, 2010).

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