Antagonistic interactions are frequently observed among bacteria in the environment, and result in complex networks, which could promote co-existence, and therefore promote biodiversity. We analysed interactions of aquatic bacteria isolated by their ability to grow in Pseudomonas isolation agar, from Churince, Cuatro Ciénegas, Mexico. In the resulting network, highly antagonistic and highly sensitive strains could be distinguished, forming a largely hierarchical structure. Most of the highly antagonistic strains belonged to the genus Pseudomonas. The network was sender determined, which means that the antagonist strains had a larger influence on its structure than the sensitive ones. Very few interactions were necessary to connect all strains, implying that the network was "small world". The network was highly nested, having a core of highly interacting strains, with which the less antagonistic or highly sensitive interact. A probabilistic model was built, that captured most features of the network. Biological interpretation of the model implied a state in which many different antagonistic mechanisms were present, and most strains were resistant to them. Our work shows that strains of Pseudomonas from the water column at Cuatro Ciénegas have the potential to interact antagonistically with many closely related strains, and that these interactions are usually not reciprocal.