  The traditional complex network approach considers only the shortest paths
from one node to another, not taking into account several other possible paths.
This limitation is significant, for example, in urban mobility studies. In this
short report, as the first steps, we present an exhaustive approach to address
that problem and show we can go beyond the shortest path, but we do not need to
go so far: we present an interactive procedure and an early stop possibility.
After presenting some fundamental concepts in graph theory, we presented an
analytical solution for the problem of counting the number of possible paths
between two nodes in complete graphs, and a depth-limited approach to get all
possible paths between each pair of nodes in a general graph (an NP-hard
problem). We do not collapse the distribution of path lengths between a pair of
nodes into a scalar number, we look at the distribution itself - taking all
paths up to a pre-defined path length (considering a truncated distribution),
and show the impact of that approach on the most straightforward distance-based
graph index: the walk/path length.
