Complex Networks and Symmetry II: Reciprocity and Evolution of World Trade

We exploit the symmetry concepts developed in the companion review of this article to introduce a stochastic version of link reversal symmetry, which leads to an improved understanding of the reciprocity of directed networks. We apply our formalism to the international trade network and show that a strong embedding in economic space determines particular symmetries of the network, while the observed evolution of reciprocity is consistent with a symmetry breaking taking place in production space. Our results show that networks can be strongly affected by symmetry-breaking phenomena occurring in embedding spaces, and that stochastic network symmetries can successfully suggest, or rule out, possible underlying mechanisms.Comment: Final accepted versio

Link creation and profile alignment in the aNobii social network

The present work investigates the structural and dynamical properties of aNobii\footnote{http://www.anobii.com/}, a social bookmarking system designed for readers and book lovers. Users of aNobii provide information about their library, reading interests and geographical location, and they can establish typed social links to other users. Here, we perform an in-depth analysis of the system's social network and its interplay with users' profiles. We describe the relation of geographic and interest-based factors to social linking. Furthermore, we perform a longitudinal analysis to investigate the interplay of profile similarity and link creation in the social network, with a focus on triangle closure. We report a reciprocal causal connection: profile similarity of users drives the subsequent closure in the social network and, reciprocally, closure in the social network induces subsequent profile alignment. Access to the dynamics of the social network also allows us to measure quantitative indicators of preferential linking.Comment: http://www.iisocialcom.org/conference/socialcom2010

GTI-space : the space of generalized topological indices

A new extension of the generalized topological indices (GTI) approach is carried out torepresent 'simple' and 'composite' topological indices (TIs) in an unified way. Thisapproach defines a GTI-space from which both simple and composite TIs represent particular subspaces. Accordingly, simple TIs such as Wiener, Balaban, Zagreb, Harary and Randićconnectivity indices are expressed by means of the same GTI representation introduced for composite TIs such as hyper-Wiener, molecular topological index (MTI), Gutman index andreverse MTI. Using GTI-space approach we easily identify mathematical relations between some composite and simple indices, such as the relationship between hyper-Wiener and Wiener index and the relation between MTI and first Zagreb index. The relation of the GTI space with the sub-structural cluster expansion of property/activity is also analysed and some routes for the applications of this approach to QSPR/QSAR are also given

How does Europe Make Its Mind Up? Connections, cliques, and compatibility between countries in the Eurovision Song Contest

We investigate the complex relationships between countries in the Eurovision Song Contest, by recasting past voting data in terms of a dynamical network. Despite the British tendency to feel distant from Europe, our analysis shows that the U.K. is remarkably compatible, or 'in tune', with other European countries. Equally surprising is our finding that some other core countries, most notably France, are significantly 'out of tune' with the rest of Europe. In addition, our analysis enables us to confirm a widely-held belief that there are unofficial cliques of countries -- however these cliques are not always the expected ones, nor can their existence be explained solely on the grounds of geographical proximity. The complexity in this system emerges via the group 'self-assessment' process, and in the absence of any central controller. One might therefore speculate that such complexity is representative of many real-world situations in which groups of 'agents' establish their own inter-relationships and hence ultimately decide their own fate. Possible examples include groups of individuals, societies, political groups or even governments