In a graph of nodes, all nodes are connected to n other nodes. Periodically a random node emits a pulse. What is the frequency with which you receive pulses from k steps away, compared to at one degree of separation from pulse emitter (k = 1)?
The connections are one-way, and the pulse propagates node to node, away from the pulse emitter. The pulse never loops.
The pulse has reached (¹+²+³+⁴+…….^k) nodes at distance k away from pulse emitter. That means a pulse reaches 1/n * (¹+²+³+⁴+…….^k) times more nodes when at distance k compared to one degree of separation from pulse emitter (k = 1). The frequency can then be calculated relative k = 1 as 1/n * (¹+²+³+⁴+…….^k), k = 1 giving the lowest frequency of 1/n * n¹ = 1.