Analysis of Ego Network Structure in Online Social Networks Valerio Arnaboldi, Marco Conti, Andrea Passarella and Fabio Pezzoni Institute of Informatics and Telematics of CNR via G. Moruzzi, 1 - 56124 Pisa, Italy Email: {v.arnaboldi, m.conti, a.passarella, f.pezzoni}@iit.cnr.it Abstract—Results about offline social networks demon- strated that the social relationships that an individual (ego) maintains with other people (alters) can be organised into different groups according to the ego network model. In this model the ego can be seen as the centre of a series of layers of increasing size. Social relationships between ego and alters in layers close to ego are stronger than those belonging to more external layers. Online Social Networks are becoming a fundamental medium for humans to manage their social life, however the structure of ego networks in these virtual environments has not been investigated yet. In this work we contribute to fill this gap by analysing a large data set of Facebook relationships. We filter the data to obtain the fre- quency of contact of the relationships, and we check - by using different clustering techniques - whether structures similar to those found in offline social networks can be observed. The results show a strikingly similarity between the social structures in offline and Online Social Networks. In particular, the social relationships in Facebook share three of the most important features highlighted in offline ego networks: (i) they appear to be organised in four hierarchical layers; (ii) the sizes of the layers follow a scaling factor near to three; and (iii) the number of active social relationships is close to the well-known Dunbar’s number. These results strongly suggest that, even if the ways to communicate and to maintain social relationships are changing due to the diffusion of Online Social Networks, the way people organise their social relationships seems to remain unaltered. I. I NTRODUCTION We are seeing a very significant process of integration between the physical world of the users of ICT technologies, and the cyber (virtual) world formed by the broad range of Internet applications. This is particularly evident in the area of social networks. Online Social Networks (OSNs) and offline social networks - which represent the social networks formed by the users due to personal interactions in the physical world - definitely influence each other. People become friends in OSNs with individuals they also know “in the real life”, while OSNs can be a means of reinforcing and maintaining social relationships existing in the physical world. Facebook, Twitter and many other OSNs have introduced a set of new communication mechanisms that are becoming part of the way in which we interact socially. Although several aspects are still under investigation, key properties regarding offline social networks have been investigated quite extensively (e.g., the difference between strong and weak ties and the importance of the latter [1], the structural properties of the network [2], just to mention a few examples). On the other hand, the analysis of the properties of OSNs is much less advanced. The interplay between social interactions in the two types of networks is only partially understood and still under investigation [3], [4]. Moreover, the structural properties of OSNs, and their differences and similarities with offline social networks are not yet fully understood. In this paper we focus on the latter aspect, provid- ing a characterisation of structural properties of Facebook networks, and comparing them with well known results available in the anthropology literature about offline social networks’ structure [2]. Our results provide two major contributions. On the one hand, we contribute to better characterise OSNs per se. On the other hand, we compare equivalent properties on OSNs and offline social networks, thus contributing to better understanding similarities and differences of social structures in the cyber and physical worlds. Assessing such similarities can be very useful also to exploit OSNs to better understand some offline social networks’ properties. For example, collecting data regarding offline social networks is a rather difficult task, which involves lengthy processes to distribute, compile and collect questionnaires. Studying similar properties on OSNs would clearly be much simpler and quicker. In this work, we focus on characterising the properties of ego networks in OSNs. While a lot of work has been done to describe the global structure of OSNs [5]–[7], the study of ego networks in virtual environments has received little attention so far. Ego networks are social networks made up of an individual (called ego) along with all the social ties she has with other people (called alters). Ego networks are an important subject of investigation in anthropology, as several fundamental properties of social relationships can be characterised by studying them. In particular, it has been shown that in (offline) ego networks there are a series of “circles” of alters arranged in a hierarchical inclusive sequence based on an increasing level of intimacy [8], [9]. The inner-most circle includes alters with a very strong rela- tionship with the ego. Each subsequent circle (in hierarchy)