  We introduce a new graph parameter called the burning number, inspired by
contact processes on graphs such as graph bootstrap percolation, and graph
searching paradigms such as Firefighter. The burning number measures the speed
of the spread of contagion in a graph; the lower the burning number, the faster
the contagion spreads. We provide a number of properties of the burning number,
including characterizations and bounds. The burning number is computed for
several graph classes, and is derived for the graphs generated by the Iterated
Local Transitivity model for social networks.
