Application of the theory of networks to model a drainage network of a watershed: case study Department of Quindío Colombia

Background: The hydrographic network of the basins of the department of Quindio, located in Colombia, South America, suffers from pollution due to industries such as tanneries, mining, food processing, among others. Goals: Represent a hydrographic network of a basin employing a graph and study its most representative measures of centrality; as a case study, we considered the hydrologic network of the basins of the department of Quindio. Methods: The theory of networks and the analysis of centrality measures such as degree distribution, PageRank, and eccentricity; also, topological measures such as density and assortativity.  Results: The study provided a different approach to research on the properties of river networks. The grade distribution shows a network with input grades of one, two, and three, while the output grade is only one or zero, consistent with a typical mountain basin. Measurements such as density and assortativity showed a low-density network with no defined connection patterns. The centrality of PageRank and eccentricity highlighted the leading causes and the most important rivers according to the way the hydrographic network is connected. Conclusions: The study concluded that by using network theory, we obtained a global vision of the network, understanding its structure and allowing us to visualize which areas of the network are vulnerable. PageRank’s centrality allowed us to identify well-monitored nodes in the network and those that need care; this same distribution highlighted zones in the network that are more prone to contamination. Finally, the eccentricity determined the center of the network (sector of “La Maria”) as one of the network’s most vulnerable areas.