Evidence of structural balance in spatial ecological networks

of these networks presents some difficulties over the analysis of networks with only one type of interactions, being necessary the use of new methodologies or theoretical frameworks (like the use of multilayer networks, Mucha et al. 2010, Boccaletti et al. 2014, Kivelä et al. 2014). Networks which include positive and negative links are called signed networks and have been mostly considered theoretically (Harary et al. 1953, Zaslavsky 1982, Traag and Bruggeman 2009) and used to study social networks (Leskovec et al. 2010, Szell and Thurner 2010, Szell et al. 2010, Facchetti et al. 2011), while being ignored in other contexts such as ecological systems. Signed networks exhibit a property called structural balance, which is based on how nodes organize in subgroups within the network (Cartwright and Harary 1956). A signed network is said to be balanced if it can be partitioned into groups of nodes in such a way that 1) every pair of connected nodes within the same group share a positive link, and 2) links between nodes within different groups have a negative sign (Doreian and Mrvar 2009). Structural balance is associated with the resilience of social networks because it prevents the appearance of conflicts that might disrupt the system (Cartwright and Harary 1956). However, real networks rarely organize in a perfectly balanced way (i.e. some links do not fulfill the criterion for structural balance), and the deviation from perfect balance is called ‘frustration’ Ecography 40: 733–741, 2017 doi: 10.1111/ecog.02561 © 2016 The Authors. Ecography © 2016 Nordic Society Oikos Subject Editor: Miguel Araújo. Editor-in-Chief: Miguel Araújo. Accepted 14 May 2016