 
Summary: Determining the distance to monotonicity of a biological network:
a graphtheoretical approach
G. Iacono
, F. Ramezani
, N. Soranzo
and C. Altafini
SISSA Int. School for Advanced Studies
via Beirut 24, 34014 Trieste, Italy
MaxPlanckInstitut fšur Informatik,
Stuhlsatzenhausweg 85, 66123 Saarbršucken, Germany
August 31, 2009
Abstract
We use ideas from graph theory in order to determine how distant is a given biological
network from being monotone. On the signed graph representing the system, the minimal
number of sign inconsistencies (i.e., the distance to monotonicity) is shown to be equal to the
minimal number of fundamental cycles having a negative sign. Suitable operations aiming
at computing such number are also proposed and shown to outperform all algorithms so far
existing for this task.
