Past exam of the year 1 of the computer science course of the University of Oxford / 2013 / Functional programming, design and analysis of algorithms / 5 / a

A length-zero graph path starts and ends at the same vertex. Therefore $P_0$ is the Boolean identity matrix. A graph path of length at most one is either such a stationary graph path or one original directed edge:The logical disjunction is entrywise. Diagonal entries of $E$ may be false if there are no self-loops, but every diagonal entry of $P_1$ is true because the zero-length graph path is allowed.