  Recent work has proven the existence of extreme inbreeding in a European
ancestry sample taken from the contemporary UK population \cite{nature_01}.
This result brings our attention again to a math problem related to inbreeding
family trees and diversity. Groups with a finite number of individuals could
give a variety of genetic relationships. { In previous works
\cite{PhysRevE.92.052132, PhysRevE.90.022125, JARNE20191}, we have addressed
the issue of building inbreeding trees for biparental reproduction using
Markovian models. Here, we extend these studies by presenting an algorithm to
generate and represent inbreeding trees with no overlapping generations. We
explicitly assume a two-gender reproductory scheme, and we pay particular
attention to the links between nodes. We show that even for a simple case with
a relatively small number of nodes in the tree, there are a large number of
possible ways to rearrange the links between generations. We present an
open-source python code to generate the tree graph, the adjacency matrix, and
the histogram of the links for each different tree representation. We show how
this mapping reflects the difference between tree realizations, and how
valuable information may be extracted upon inspection of these matrices. The
algorithm includes a feature to average several tree realizations, obtain the
connectivity distribution, and calculate the average and mean value. We used
this feature to compare trees with a different number of generations and nodes.
The code presented here, available in Git-Hub, may be easily modified to be
applied to other areas of interest involving connections between individuals,
extend the study to add more characteristics of the different nodes, etc.
