  We use observed transmission line outage data to make a Markov influence
graph that describes the probabilities of transitions between generations of
cascading line outages, where each generation of a cascade consists of a single
line outage or multiple line outages. The new influence graph defines a Markov
chain and generalizes previous influence graphs by including multiple line
outages as Markov chain states. The generalized influence graph can reproduce
the distribution of cascade size in the utility data. In particular, it can
estimate the probabilities of small, medium and large cascades. The influence
graph has the key advantage of allowing the effect of mitigations to be
analyzed and readily tested, which is not available from the observed data. We
exploit the asymptotic properties of the Markov chain to find the lines most
involved in large cascades and show how upgrades to these critical lines can
reduce the probability of large cascades.
