We propose a procedure for analyzing and characterizing complex networks. We apply this to the social network as constructed from email communications within a medium sized university with about 1700 employees. Email networks provide an accurate and nonintrusive description of the flow of information within human organizations. Our results reveal the self-organization of the network into a state where the distribution of community sizes is self-similar. This suggests that a universal mechanism, responsible for emergence of scaling in other self-organized complex systems, as, for instance, river networks, could also be the underlying driving force in the formation and evolution of social networks. DOI: 10.1103/PhysRevE.68.065103 PACS number͑s͒: 89.75.Fb, 89.75.Da, 89.75.Hc Signatures of complex systems appear in disciplines as diverse as biology, chemistry, economy, and computer science, to name just a few. More specifically, the study of the complex networks of interactions in such systems has received a lot of attention from the statistical physics community ͓1-5͔. The structure of these complex networks is a reflection of the dynamics of their formation and evolution, and can be partially characterized using statistical observables such as the average distance between nodes ͓1͔, the clustering coefficient ͓1͔, and the degree distribution ͓2,3͔. Even though these measures are very useful in some situations, often they are not sufficient to describe key features of networks. In the specific field of social sciences, a more detailed description of human interactions is crucial to understand the formation and evolution of complex social networks. In this paper we describe a procedure to characterize the structure of networks, based on a recently proposed algorithm to identify communities in graphs ͓6͔. Our procedure allows one to study quantitatively the hierarchical structure of nested communities in networks. Moreover we apply the procedure to a real social network. We define and analyze the complex email network of an organization with about 1700 employees and determine its community structure. Our results reveal that this network self-organizes into a selfsimilar structure, suggesting that some universal mechanism could be the underlying driving force in the formation and evolution of social networks, as happens in other complex systems ͓7,8͔. Apart from work related reasons, ties between individuals in any organization arise, without external influence, due to personal, political, and cultural reasons, among others. The rapid development of electronic communications provides a powerful tool to analyze the informal self-organized social network arising as a result of the formation of such ties. Indeed, every time an email is sent, the addresses of the sender and the receiver are routinely registered in a server. Therefore, an email network can be built regarding each email address as a node and linking two nodes if there is an email communication between them. We take as a case study the email network of University at Rovira i Virgili ͑URV͒ in Tarragona, Spain, containing 1669 users including faculty, researchers, technicians, managers, administrators, and graduate students. Bulk emails provide little or no information about how individuals or teams interact, so to minimize their effect: ͑i͒ we eliminate emails that are sent to more than 50 different recipients and ͑ii͒ we disregard links that are unidirectional, that is, we consider that two nodes A and B are connected only if A has sent an email to B and B has also sent an email to A. With these restrictions, the network is an undirected graph ͓26͔. The cumulative degree distribution P(k) of the email network-representing the probability that a node has k or more links to other nodes-is exponential P͑k ͒ϰexp͑ Ϫk/k*͒ ͑1͒ for kу2, with k*ϭ9.2. This result is in contrast with recent findings indicating that some technology based social networks-such as rough email networks ͓9͔, the instant messaging network ͓10͔, or the PGP ͑pretty good privacy͒ encryption network ͓11͔-which show heavily skewed degree distributions, but is consistent with the proposal of Amaral and co-workers that the truncation of the scale-free behavior in real world networks is due to the existence of limitations or costs in the establishment of connections ͓3,12͔. Indeed, it seems plausible that there are costs to maintaining active social acquaintances and therefore active communications. However, it is relatively easy to keep many electronic acquaintances open, although most of them are probably inactive from a social point of view. Out of the total 1669 nodes, 1133 belong to the giant component. The rest are isolated or, at most, connected by pairs. In the following, we focus on this giant component that can be characterized by statistical properties such as its clustering coefficient Cϭ0.254 and its average shortest path length dϭ3.606 ͓1͔. For comparison, we construct a random network with exactly the same exponential degree distribution as the email network following the procedure proposed in Ref. ͓13͔ ͑from now on we will call it random exponential PHYSICAL REVIEW E 68, 065103͑R͒ ͑2003͒
Studies of the community structure of email networks have also been conducted by Guimerà et al. REF using emails in a university.
Self-similar community structure in a network of human interactions
Physical review. E, Statistical, nonlinear, and soft matter physics
Physical review. E, Statistical, nonlinear, and soft matter physics
Medicine Physics