Complex networks are used to describe interactions in many real world systems, including economic, biological and social systems. An analysis was done of inter-student friendship, enmity and kinship relationships at three elementary schools by building social networks of these relationships and studying their properties. Friendship network measurements were similar between schools and produced a Poisson topology with a high clustering index. Enmity network measurements were also similar between schools and produced a power law topology. Spatial confinement and the sense of belonging to a social group played vital roles in shaping these networks. Two models were developed which generate complex friendship and enmity networks that reproduce the properties observed at the three studied elementary schools.

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The Ring of Cenotes (RC) is an alignment of numerous cenotes (sinkholes) in a semicircular form (with a radius of 100 km) located in northwestern Yucatán, México. The formation roughly coincides with a concentric ring that corresponds to a buried structure, which has been identified as the product of a meteor impact, known as the Chicxulub crater. Secondary permeability generated by the fracturing and faulting of the sedimentary sequence in the Chicxulub crater has favored the karstification process and therefore the development of underground rivers that transport water from the mainland to the sea. This study implements the network theory to study the hydrological connectivity between a group of 11 cenotes within the RC. Eight electrical resistivity tomography transects were used as an empirical basis. Each transect was acquired directly in the field using the SuperSting R1/IP equipment with a dipole-dipole configuration. An adapted version of the reliability algorithm for communication networks was used as a theoretical model. We found evidence of the existence of water cavities in the study area. We made a network from the data and assigned connection probabilities among cenotes as a function of the separation length and the number of water cavities, as well as their size.