Factors Determining Nestedness in Complex Networks

Understanding the causes and effects of network structural features is a key task in deciphering complex systems. In this context, the property of network nestedness has aroused a fair amount of interest as regards ecological networks. Indeed, Bastolla et al. introduced a simple measure of network nestedness which opened the door to analytical understanding, allowing them to conclude that biodiversity is strongly enhanced in highly nested mutualistic networks. Here, we suggest a slightly refined version of such a measure of nestedness and study how it is influenced by the most basic structural properties of networks, such as degree distribution and degree-degree correlations (i.e. assortativity). We find that most of the empirically found nestedness stems from heterogeneity in the degree distribution. Once such an influence has been discounted – as a second factor – we find that nestedness is strongly correlated with disassortativity and hence – as random networks have been recently found to be naturally disassortative – they also tend to be naturally nested just as the result of chance.This work was supported by Junta de Andalucia projects FQM-01505 and P09-FQM4682, and by Spanish MEC-FEDER project FIS2009-08451. S.J. is grateful for financial support from the European Commision under the Marie Curie Intra-European Fellowship Programme PIEF-GA-2010-276454

Isocyanide substitution in octadecacarbonyl hexaosmium

The crystal structures of the two isocyanide substituted hexaosmium clusters, Os6 (CO)18 (CNC6 H4 Me)2 and Os6 (CO)16 (CNCMe3)2 are reported. The former involves both a triple bridging and a terminal isonitrile group whilst the latter is related to the parent carbonyl Os6 (CO)18. The molecular structures are discussed in terms of electronic inequivalences within the metal cluster framework