Degree correlations in signed social networks

We investigate degree correlations in two online social networks where users are connected through different types of links. We find that, while subnetworks in which links have a positive connotation, such as endorsement and trust, are characterized by assortative mixing by degree, networks in which links have a negative connotation, such as disapproval and distrust, are characterized by disassortative patterns. We introduce a class of simple theoretical models to analyze the interplay between network topology and the superimposed structure based on the sign of links. Results uncover the conditions that underpin the emergence of the patterns observed in the data, namely the assortativity of positive subnetworks and the disassortativity of negative ones. We discuss the implications of our study for the analysis of signed complex networks

Multirelational Organization of Large-scale Social Networks in an Online World

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 in empirical studies, 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 proceed to 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.Comment: 7 pages, 5 figures, accepted for publication in PNA

Structure and evolution of a European Parliament via a network and correlation analysis

We present a study of the network of relationships among elected members of the Finnish parliament, based on a quantitative analysis of initiative co-signatures, and its evolution over 16 years. To understand the structure of the parliament, we constructed a statistically validated network of members, based on the similarity between the patterns of initiatives they signed. We looked for communities within the network and characterized them in terms of members' attributes, such as electoral district and party. To gain insight on the nested structure of communities, we constructed a hierarchical tree of members from the correlation matrix. Afterwards, we studied parliament dynamics yearly, with a focus on correlations within and between parties, by also distinguishing between government and opposition. Finally, we investigated the role played by specific individuals, at a local level. In particular, whether they act as proponents who gather consensus, or as signers. Our results provide a quantitative background to current theories in political science. From a methodological point of view, our network approach has proven able to highlight both local and global features of a complex social system.Comment: 15 pages, 10 figure

Social Stability and Extended Social Balance - Quantifying the Role of Inactive Links in Social Networks

Structural balance in social network theory starts from signed networks with active relationships (friendly or hostile) to establish a hierarchy between four different types of triadic relationships. The lack of an active link also provides information about the network. To exploit the information that remains uncovered by structural balance, we introduce the inactive relationship that accounts for both neutral and nonexistent ties between two agents. This addition results in ten types of triads, with the advantage that the network analysis can be done with complete networks. To each type of triadic relationship, we assign an energy that is a measure for its average occupation probability. Finite temperatures account for a persistent form of disorder in the formation of the triadic relationships. We propose a Hamiltonian with three interaction terms and a chemical potential (capturing the cost of edge activation) as an underlying model for the triadic energy levels. Our model is suitable for empirical analysis of political networks and allows to uncover generative mechanisms. It is tested on an extended data set for the standings between two classes of alliances in a massively multi-player on-line game (MMOG) and on real-world data for the relationships between countries during the Cold War era. We find emergent properties in the triadic relationships between the nodes in a political network. For example, we observe a persistent hierarchy between the ten triadic energy levels across time and networks. In addition, the analysis reveals consistency in the extracted model parameters and a universal data collapse of a derived combination of global properties of the networks. We illustrate that the model has predictive power for the transition probabilities between the different triadic states.Comment: 21 pages, 10 figure