  Understanding which system structure can sustain stable dynamics is a
fundamental step in the design and analysis of large scale dynamical systems.
Towards this goal, we investigate here the structural stability of systems with
a random structure. As is usually done, we describe the system's structure
through a graph describing interactions between parts of the system, and we
call a graph stable if it describe a structurally stable system, i.e., a system
which can sustain stable dynamics. We then consider two Erdos-Renyi random
graph models, and we obtain for each the probability that a graph sampled from
these models is structurally stable.
