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...onal social-dynamics hypotheses. The Pardus data allows for direct empirical testing of long-standing hypotheses on social network dynamics, such as the Hypothesis of triadic closure (Rapoport, 1953; =-=Granovetter, 1973-=-), the Weak ties hypothesis (Granovetter, 1973), or the Hypothesis of social balance (Harary, 1953; Doreian and Mrvar, 1996). For quantification purposes we employ network measures such as betweenness...

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... due to the large amount of strong mutual influences, naturally present in systems of such high complexity. 3. Networks 3.1. Definitions Graph In mathematical terms, networks are described by graphs (=-=Wasserman and Faust, 1994-=-; Dorogovtsev and Mendes, 2003). An undirected graph G = (N ,L) is defined as a pair of sets, the node setN containing all nodes ni and the link set L containing unordered pairs lij := {ni, nj} denoti...

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...e, i.e. a directed triad is complete if it contains no null dyads, it is incomplete otherwise. having identical in/out degrees and equally likely numbers of mutual dyads for each node (Roberts, 2000; =-=Milo et al., 2002-=-). Statistical significance of a triad class i is measured by the Z score Zi = (N reali − N̄ randi ) std(N randi ) , (11) where N reali is the frequency of occurence of the triad class in the consider...

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...me resolved studies of an internet dating community (Holme et al., 2004), the analysis of a university email network (Kossinets and Watts, 2006), of the web of scientific coauthorships (Ravasz, 2004; =-=Newman, 2001-=-, 2004), as well as several large-scale networks of various types (Leskovec et al., 2007). Network growth and re-linking processes can be directly studied and compared to well-known models, such as e....

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... strong mutual influences, naturally present in systems of such high complexity. 3. Networks 3.1. Definitions Graph In mathematical terms, networks are described by graphs (Wasserman and Faust, 1994; =-=Dorogovtsev and Mendes, 2003-=-). An undirected graph G = (N ,L) is defined as a pair of sets, the node setN containing all nodes ni and the link set L containing unordered pairs lij := {ni, nj} denoting those nodes which are conne...

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...ies hypothesis (Granovetter, 1973), or the Hypothesis of social balance (Harary, 1953; Doreian and Mrvar, 1996). For quantification purposes we employ network measures such as betweenness centrality (=-=Freeman, 1977-=-) and overlap which measures how often a given pair of nodes has links to other common nodes (Onnela et al., 2007). To our knowledge, no longitudinal measurements of largescale signed networks exist a...

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...ensity which is not possible with r∗ (Garlaschelli and Loffredo, 2004). Assortativity Assortative mixing coefficients are the Pearson correlation coefficients of the degrees at either ends of a link (=-=Newman, 2002-=-): r = ktokfrom − ktokfrom√ k2to − kto 2 √ k2from − kfrom 2 ∈ [−1, 1]. (8) Bars denote averages, kto and kfrom index the (in-, out- or undirected) degrees of nodes at the beginning and end of links, r...

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...ciency is a reasonable approximation for the inverse geodesic in unweighted graphs; local efficiency is a good approximation for the clustering coefficient when most local networks Gi are not sparse (=-=Latora and Marchiori, 2001-=-). Reciprocity Reciprocity measures the tendency of individuals to reciprocate connections, i.e. the creation of mutual instead of asymmetric dyads (Wasserman and Faust, 1994). Following Holme et al. ...

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...tforward fashion. These ‘stylized’ facts, such as volatility clustering, fat-tailed return distributions, squared autocorrelation decays, etc., are known in detail for traded goods in the real world (=-=Cont, 2001-=-). Further, co-evolution dynamics, i.e. the evolution of economic properties of players (e.g. wealth) as a function of their local social networks, and vice versa, their social evolution as a function...

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...gle or at best small numbers of network snapshots. Important exceptions include time resolved studies of an internet dating community (Holme et al., 2004), the analysis of a university email network (=-=Kossinets and Watts, 2006-=-), of the web of scientific coauthorships (Ravasz, 2004; Newman, 2001, 2004), as well as several large-scale networks of various types (Leskovec et al., 2007). Network growth and re-linking processes ...

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...e triad ninjnk is defined to be balanced if the product of signs sijsjkski = 1, and is unbalanced otherwise. Members of a balanced complete triad thus fulfill the following adage (Antal et al., 2006; =-=Heider, 1946-=-): – a friend of my friend is my friend – a friend of my enemy is my enemy – an enemy of my friend if my enemy – an enemy of my enemy is my friend In physics the first statement corresponds to a ferro...

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...derstood if and how communities show aging effects, such as densification, i.e. shrinking diameters and growing average degrees. This phenomenon has been observed in societies and online communities (=-=Leskovec et al., 2007-=-, 2008), as well as in the evolution of scientific fields and cities (Bettencourt et al., 2007, 2008). The vast majority of social network studies analyze single or at best small numbers of network sn...

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...e or negative relationship (Doreian and Mrvar, 1996). We write sij short for σ(lij), and set sij := 0 when lij does not exist. Every signed digraph has a valency matrix V with entries vij defined as (=-=Harary et al., 1965-=-): vij = o if sij = sji = 0 vij = p if sij + sji > 0 vij = n if sij + sji < 0 vij = a otherwise (1) These entries correspond to null (o) dyads, to dyads with only positive ties (p) , to dyads with onl...

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...2009), and appear in a model of growing social networks (Jin et al., 2001). Note that C/Cr has a high value for friend networks (C/Cr > 100), as is expected for most social networks of positive ties (=-=Newman and Park, 2003-=-). Positive reciprocity All networks are reciprocal, fig. 10 (j). At the last day the PM network has a reciprocity of ρ ≈ 0.80, the friend network has ρ ≈ 0.68 after having reached a maximum of ρ ≈ 0....

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...arabási and Albert, 1999) or static relinking models (Thurner et al., 2007). Preferential attachment dynamics of real-world networks have been verified in a few recent studies (Csárdi et al., 2007; =-=Leskovec et al., 2008-=-; Jeong et al., 2003). 2. Testing traditional social-dynamics hypotheses. The Pardus data allows for direct empirical testing of long-standing hypotheses on social network dynamics, such as the Hypoth...

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...ional methods of social science such as interviews and questionnaires do not only need a lot of time and resources to deliver statistically meaningful assertions, but may introduce well-known biases (=-=Carrington et al., 2005-=-). To many it might seem clear that social sciences can not overcome these problems, and that therefore social sciences would always remain on a lower quantitative and qualitative level than the natur...

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...ta, and the possibility to take simultaneous measurements on subjects and their surroundings, might appear in a radically more positive light when looking at massive multiplayer online games (MMOGs) (=-=Castronova, 2005-=-). Such computer games not only allow to conduct complete measurements of socially interacting humans, they also provide data at rates comparable to physical experiments. Remarkably, one of the larges...

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... far from conclusive due to limited data and small scales (10 to 100 nodes), and a low number of samples (about ≈ 10 observations). Further, the extent of reciprocity and Triad significance profiles (=-=Milo et al., 2004-=-) together with their dynamics can be directly accessed from the game data. For the quantification of these concepts we use recent technology developed in the context of motif distributions. To unders...

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...ypotheses on social network dynamics, such as the Hypothesis of triadic closure (Rapoport, 1953; Granovetter, 1973), the Weak ties hypothesis (Granovetter, 1973), or the Hypothesis of social balance (=-=Harary, 1953-=-; Doreian and Mrvar, 1996). For quantification purposes we employ network measures such as betweenness centrality (Freeman, 1977) and overlap which measures how often a given pair of nodes has links t...

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...y analyzed from a network perspective (Onnela et al., 2007; Lambiotte et al., 2008). While there exists some insight into real-world friend networks in the literature, e.g. of the Facebook community (=-=Golder et al., 2007-=-), there is practically no knowledge of topology and dynamics of enemy networks (Labianca and Brass, 2006). Since the time resolution of our data is accurate to one second, it becomes possible to stud...

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... findings within ‘specialist’ communities. From a scientific point of view online games provide a tool for understanding collective human phenomena and social dynamics on an entirely different scale (=-=Bainbridge, 2007-=-; Castronova, 2006). In these games all information about all actions taken by all players can be easily recorded and stored in log-files at practically no cost. This quantity of data has been unthink...

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...networks. Decreasing clustering coefficients have been reported for coauthorship networks (Ravasz, 2004), online social networks (Hu and Wang, 2009), and appear in a model of growing social networks (=-=Jin et al., 2001-=-). Note that C/Cr has a high value for friend networks (C/Cr > 100), as is expected for most social networks of positive ties (Newman and Park, 2003). Positive reciprocity All networks are reciprocal,...

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...99) or static relinking models (Thurner et al., 2007). Preferential attachment dynamics of real-world networks have been verified in a few recent studies (Csárdi et al., 2007; Leskovec et al., 2008; =-=Jeong et al., 2003-=-). 2. Testing traditional social-dynamics hypotheses. The Pardus data allows for direct empirical testing of long-standing hypotheses on social network dynamics, such as the Hypothesis of triadic clos...

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...sts some insight into real-world friend networks in the literature, e.g. of the Facebook community (Golder et al., 2007), there is practically no knowledge of topology and dynamics of enemy networks (=-=Labianca and Brass, 2006-=-). Since the time resolution of our data is accurate to one second, it becomes possible to study time courses of global network properties. This way it can be understood if and how communities show ag...

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...7). To our knowledge, no longitudinal measurements of largescale signed networks exist as of today. One well-known social network study on monks in a monastery can be found in the classic literature (=-=Sampson, 1968-=-), as well as a modern long-time survey of social dynamics in classrooms (Jordán, 2009). These are first attempts of systematic social balance experiments, however being far from conclusive due to li...

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...7, 2008). The vast majority of social network studies analyze single or at best small numbers of network snapshots. Important exceptions include time resolved studies of an internet dating community (=-=Holme et al., 2004-=-), the analysis of a university email network (Kossinets and Watts, 2006), of the web of scientific coauthorships (Ravasz, 2004; Newman, 2001, 2004), as well as several large-scale networks of various...

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... Testing traditional social-dynamics hypotheses. The Pardus data allows for direct empirical testing of long-standing hypotheses on social network dynamics, such as the Hypothesis of triadic closure (=-=Rapoport, 1953-=-; Granovetter, 1973), the Weak ties hypothesis (Granovetter, 1973), or the Hypothesis of social balance (Harary, 1953; Doreian and Mrvar, 1996). For quantification purposes we employ network measures ...

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...inguish between reciprocal (ρ > 0), areciprocal (ρ = 0) and antireciprocal (ρ < 0) networks. Further, ρ enables a clear ordering of networks independent of link density which is not possible with r∗ (=-=Garlaschelli and Loffredo, 2004-=-). Assortativity Assortative mixing coefficients are the Pearson correlation coefficients of the degrees at either ends of a link (Newman, 2002): r = ktokfrom − ktokfrom√ k2to − kto 2 √ k2from − kfrom...

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...fact that all players are engaged in economic activities allows for statistically significant measurements of wealth and income distributions which can be compared to real economies (Yakovenko, 2009; =-=Dragulescu and Yakovenko, 2001-=-; Chatterjee et al., 2007). The process of price formation – and more generally preference relations – for all goods and services in the game can be observed within the social and economical context o...

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...ocial network dynamics, such as the Hypothesis of triadic closure (Rapoport, 1953; Granovetter, 1973), the Weak ties hypothesis (Granovetter, 1973), or the Hypothesis of social balance (Harary, 1953; =-=Doreian and Mrvar, 1996-=-). For quantification purposes we employ network measures such as betweenness centrality (Freeman, 1977) and overlap which measures how often a given pair of nodes has links to other common nodes (Onn...

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...ally conclusive quantitative statement, visual inspection clearly reveals that growth is super-linear, fig. 11. Network densification has previously been studied under the name of accelerated growth (=-=Dorogovtsev and Mendes, 2001-=-, 2003). Growing average degrees were observed in all three time evolution studies of growing networks we are aware of (Holme et al., 2004; Leskovec et al., 2007; Ravasz, 2004). From decreasing distan...

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...er@univie.ac.at (Stefan Thurner) URL: http://complex-systems.meduniwien.ac.at (Stefan Thurner) mathematical methods and physical concepts. Second, data is of comparably poor availability and quality (=-=Watts, 2007-=-; Lazer et al., 2009). Evidently it is much harder to obtain data from social systems than from repeatable experiments on (non-complex) physical systems. Despite these severe problems, it is neverthel...

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...eflexive closure, i.e. a directed triad is complete if it contains no null dyads, it is incomplete otherwise. having identical in/out degrees and equally likely numbers of mutual dyads for each node (=-=Roberts, 2000-=-; Milo et al., 2002). Statistical significance of a triad class i is measured by the Z score Zi = (N reali − N̄ randi ) std(N randi ) , (11) where N reali is the frequency of occurence of the triad cl...

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... or structural, balance has been generalized to an arbitrary amount of subjects by Cartwright and Harary (1956); hypotheses about the evolution of social balance have been conjectured (Doreian, 2004; =-=Doreian and Mrvar, 2009-=-). We measure the evolution of social balance by using optimizational partition algorithms implemented in Pajek9. Here we face three concrete problems: (i) Algorithmic complexity: Due to algorithmic c...

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...idence that online game communities may serve as a model for real world communities. It is not obvious a priori that a population of online players is a representative sample of real-world societies (=-=Williams et al., 2009-=-). However, several recent studies are providing evidence that human behavior on a collective level is remarkably robust, meaning that statistical differences of real-world communities and gamesocieti...

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...er (1946). A complete triad ninjnk is defined to be balanced if the product of signs sijsjkski = 1, and is unbalanced otherwise. Members of a balanced complete triad thus fulfill the following adage (=-=Antal et al., 2006-=-; Heider, 1946): – a friend of my friend is my friend – a friend of my enemy is my enemy – an enemy of my friend if my enemy – an enemy of my enemy is my friend In physics the first statement correspo...

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.../Cr curves of PM networks fall between the curves of enemy and friend networks. Decreasing clustering coefficients have been reported for coauthorship networks (Ravasz, 2004), online social networks (=-=Hu and Wang, 2009-=-), and appear in a model of growing social networks (Jin et al., 2001). Note that C/Cr has a high value for friend networks (C/Cr > 100), as is expected for most social networks of positive ties (Newm...

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...ent studies are providing evidence that human behavior on a collective level is remarkably robust, meaning that statistical differences of real-world communities and gamesocieties are often marginal (=-=Johnson et al., 2009-=-; Jiang et al., 2009). The paper is organized as follows. In section 2 we present the game, describe the sample of players and explain their modes of communication. We introduce the three types of soc...

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...cial networks, and vice versa, their social evolution as a function of their economic network, can be extracted from the data. The theoretical literature on co-evolving networks is relatively sparse (=-=Biely et al., 2007-=-, 2009); to our knowledge there exist practically no measurements on this issue so far. 4. Group formation and dynamics – gender and country aspects. Players have the possibility to create and join ‘a...

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...work growth and re-linking processes can be directly studied and compared to well-known models, such as e.g. the preferential attachment model (Barabási and Albert, 1999) or static relinking models (=-=Thurner et al., 2007-=-). Preferential attachment dynamics of real-world networks have been verified in a few recent studies (Csárdi et al., 2007; Leskovec et al., 2008; Jeong et al., 2003). 2. Testing traditional social-d...

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...ing evidence that human behavior on a collective level is remarkably robust, meaning that statistical differences of real-world communities and gamesocieties are often marginal (Johnson et al., 2009; =-=Jiang et al., 2009-=-). The paper is organized as follows. In section 2 we present the game, describe the sample of players and explain their modes of communication. We introduce the three types of social networks studied...

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...ons include time resolved studies of an internet dating community (Holme et al., 2004), the analysis of a university email network (Kossinets and Watts, 2006), of the web of scientific coauthorships (=-=Ravasz, 2004-=-; Newman, 2001, 2004), as well as several large-scale networks of various types (Leskovec et al., 2007). Network growth and re-linking processes can be directly studied and compared to well-known mode...

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...ic analysis. The fact that all players are engaged in economic activities allows for statistically significant measurements of wealth and income distributions which can be compared to real economies (=-=Yakovenko, 2009-=-; Dragulescu and Yakovenko, 2001; Chatterjee et al., 2007). The process of price formation – and more generally preference relations – for all goods and services in the game can be observed within the...

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...ad of the absence of a completing third link, its presence should cause cognitive dissonance (however, note that a complete triad with only negative links may be seen as ambiguous concerning balance (=-=Doreian, 2004-=-)). Thus triad classes 1–6 should be overrepresented, triad classes 7–13 underrepresented in enemy networks. For friend and PM networks, excellent agreement is found with Granovetter’s prediction: Tri...

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...y or disassortativity after a transient phase of falling assortativity. Note that by using an assortativity profile it is possible to uncover families of networks, similar to TSPs (Milo et al., 2004; =-=Foster et al., 2009-=-). Structural change of PM networks due to times of war On day 422 a war between a substantial number of players broke out in the game universe. A structural change of PM networks is identifiable, mos...