In Yanofsky and Mannucci's Quantum Computing for Computer Scientists, page 80, it is said, when referring to a probabilistic dynamical system modeled by a (finite) graph, that
We shall restrict our attention to weighted graphs that satisfy the following two conditions: a) the sum of all the weights leaving a vertex is 1 and b) the sum of all the weights entering a vertex is 1. This will correspond to the fact that the marble must both go and come from someplace (there might be loops).
I understand why the fact that the marbles must go someplace requires condition a), but I don't understand why b) is required for the marbles to come from (or go) someplace.
Why is b) necessary for the marble to come from (or go) someplace?
Happy to provide more detail on my thoughts, if necessary or desired.
¡Besos, matematicos!