Protracted conflict is one of the largest human challenges that have persistently undermined economic and social progress. In recent years, there has been increased emphasis on using statistical and physical science models to better understand both the universal patterns and the underlying mechanics of conflict. Whilst macroscopic power-law fractal patterns have been shown for death-toll in wars and self-excitation models have been shown for roadside ambush attacks, very few works deal with the challenge of complex dynamics between gangs at the intra-city scale. Here, based on contributions to the historical memory of the conflict in Colombia, Medellin's gang-confrontation-network is presented. It is shown that socio-economic and violence indexes are moderate to highly correlated to the structure of the network. Specifically, the death-toll of conflict is strongly influenced by the leading eigenvalues of the gangs' conflict adjacency matrix, which serves a proxy for unstable self-excitation from revenge attacks. The distribution of links based on the geographic distance between gangs in confrontation leads to the confirmation that territorial control is a main catalyst of violence and retaliation among gangs. As a first attempt to explore the time evolution of the confrontation network, the Boltzmann-Lotka-Volterra (BLV) dynamic interaction network analysis is applied to quantify the spatial embeddedness of the dynamic relationship between conflicting gangs in Medellin. However, the non-stationary character of the violence in Medellin during the observation period restricts the application of the BLV model and results suggest that more involved and comprehensive models are needed to described the dynamics of Medellin's armed conflict.