The capacity to collect fingerprints of individuals in online media has revolutionized the way researchers explore human society. Social systems can be seen as a non-linear superposition of a multitude of complex social networks, where nodes represent individuals and links capture a variety of different social relations. Much emphasis has been put on the network topology of social interactions, however, the multi-dimensional nature of these interactions has largely been ignored, mostly because of lack of data. Here, for the first time, we analyze a complete, multi-relational, large social network of a society consisting of the 300,000 odd players of a massive multiplayer online game. We extract networks of six different types of one-to-one interactions between the players. Three of them carry a positive connotation (friendship, communication, trade), three a negative (enmity, armed aggression, punishment). We first analyze these types of networks as separate entities and find that negative interactions differ from positive interactions by their lower reciprocity, weaker clustering and fatter-tail degree distribution. We then explore how the inter-dependence of different network types determines the organization of the social system. In particular we study correlations and overlap between different types of links and demonstrate the tendency of individuals to play different roles in different networks. As a demonstration of the power of the approach we present the first empirical large-scale verification of the long-standing structural balance theory, by focusing on the specific multiplex network of friendship and enmity relations. complex networks | multiplex relations | quantitative sociology H uman societies can be regarded as large numbers of locally interacting agents, connected by a broad range of social and economic relationships. These relational ties are highly diverse in nature and can represent e.g. the feeling a person has for another (friendship, enmity, love), communication, exchange of goods (trade) or behavioral interactions (cooperation or punishment). Each type of relation spans a social network of its own. A systemic understanding of a whole society can only be achieved by understanding these individual networks and how they influence and coconstruct each other. The shape of one network influences the topologies of the others, as networks of one type may act as a constraint, an inhibitor, or a catalyst on networks of another type of relation. For instance, the network of communications poses constraints on the network of friendships, trading networks are usually constrained to positively connoted interactions such as trust, and networks representing hostile actions may serve as a catalyst for the network of punishments. A society is therefore characterized by the superposition of its constitutive socio-economic networks, all defined on the same set of nodes. This superposition is usually called multiplex, multi-relational, multi-modal or multivariate network, see Fig. 1 . The study of small-scale multiplex networks has a long tradition in the social sciences [1] , and has been applied to areas such as homophily in social networks [2] , the effect of combined interactions on an agent's behavior [3] and the non-trivial inter-relation between family and business net- works [4] . Multiplexity is thought to play an important role in the organization of large-scale networks. For example the existence of different link types between agents explains the overlap of community structures observed in social networks, where nodes may belong to several communities, each associated to one different type of interaction [5, 6] . Methodological work on multiplex networks includes the development of multiplex community detection [7] , clustering [8] and other network analysis algorithms [9] . The role of multiple relation types in measured social networks has recently been investigated across communication media [10] , in an online game [11] , as well as in ecological networks [12] . Traditional methods of social science, such as small-scale questionnaire-based approaches, get more and more replaced by automated methods of data collection which allow for entirely different scales of analysis [13, 14, 15] . This change of scale has opened new perspectives and has the potential to radically transform our understanding of social dynamics and organization [16] . The empirical verification of social theories such as the strength of weak ties [17, 18] become possible with hitherto unthinkable levels of precision. However, this large-scale perspective suffers from the drawback of a relatively coarse-grained representation of social processes taking place between individuals and of blindness in respect to the existence of different types of social interactions. For example in most works on email [19] or mobile phone networks [17, 20] , the existence and weight of a link is determined by the volume of information exchanged between two individuals. Although
These networks are also known as multirelational, multiplex, multi-layered or multivariate networks REF .
Multirelational Organization of Large-scale Social Networks in an Online World
PNAS 107, 13636-13641 (2010)
Computer Science Physics Medicine