  Hexapeptides are increasingly applied as model systems for studying the
amyloidogenecity properties of oligo- and polypeptides. It is possible to
construct 64 million different hexapeptides from the twenty proteinogenic amino
acid residues. Today's experimental amyloid databases contain only a fraction
of these annotated hexapeptides. For labeling all the possible hexapeptides as
"amyloidogenic" or "non-amyloidogenic" there exist several computational
predictors with good accuracies. It may be of interest to define and study a
simple graph structure on the 64 million hexapeptides as nodes when two
hexapeptides are connected by an edge if they differ by only a single residue.
For example, in this graph, HIKKLM is connected to AIKKLM, or HIKKNM, or
HIKKLC, but it is not connected with an edge to VVKKLM or HIKNPM. In the
present contribution, we consider our previously published artificial
intelligence-based tool, the Budapest Amyloid Predictor (BAP for short), and
demonstrate a spectacular property of this predictor in the graph defined
above. We show that for any two hexapeptides predicted to be "amyloidogenic" by
the BAP predictor, there exists an easily constructible path of length at most
6 that passes through neighboring hexapeptides all predicted to be
"amyloidogenic" by BAP. For example, the predicted amyloidogenic ILVWIW and
FWLCYL hexapeptides can be connected through the length-6 path
ILVWIW-IWVWIW-IWVCIW-IWVCIL-FWVCIL-FWLCIL-FWLCYL in such a way that the
neighbors differ in exactly one residue, and all hexapeptides on the path are
predicted to be amyloidogenic by BAP. The symmetric statement also holds for
non-amyloidogenic hexapeptides. It is noted that the mentioned property of the
Budapest Amyloid Predictor \url{https://pitgroup.org/bap} is not proprietary;
it is also true for any linear Support Vector Machine (SVM)-based predictors.
