We study a discrete di usion process introduced in some combinatorial puzzles called Flood-It, Mad Virus or HoneyBee that can be played online and whose computational complexities have recently been studied. Originally defi ned on regular boards, we show that studying their dynamics directly on general graphs is valuable: we synthesize and extend previous results, we show how to solve Flood-It on cycles by computing a poset height and how to solve the 2-Free-Flood-It variant by computing a graph radius (ENGLISH VERSION of [11])