  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. Additionally, 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,
results suggest that more involved and comprehensive models are needed to
described the dynamics of Medellin's armed conflict.
