  An impressive effort is being placed in order to develop new strategies that
allow an efficient computation of multi-loop multi-leg Feynman integrals and
scattering amplitudes, with a particular emphasis on removing spurious
singularities and numerical instabilities. In this article, we describe an
innovative geometric approach based on graph theory to unveil the causal
structure of any multi-loop multi-leg amplitude in Quantum Field Theory. Our
purely geometric construction reproduces faithfully the manifestly causal
integrand-level behaviour of the Loop-Tree Duality representation. We found
that the causal structure is fully determined by the vertex matrix, through a
suitable definition of connected partitions of the underlying diagrams. Causal
representations for a given topological family are obtained by summing over
subsets of all the possible causal entangled thresholds that originate
connected and oriented partitions of the underlying topology. These results are
compatible with Cutkosky rules. Moreover, we found that diagrams with the same
number of vertices and multi-edges exhibit similar causal structures,
regardless of the number of loops.
