Context
I have a set of objects, which we'll call nodes, arranged within a network of inputs and outputs. The data conveyed through the network is represented as energy $E$, a form of currency for the nodes.
Now a node can only output when it recieves enough energy to surpass a threshold. When it does output, its "stash" of energy gets reset to zero and the cycle starts anew.
Problem
If we were to isolate one of these connections, we would have a node $A$ which sends energy to a node $B$. This doesn't mean node $A$ is the only input to node $B$ as there exists other nodes connected to node $B$.
I need to know the overall influence (as a percent) node $A$ has over the "activations" of node $B$. With the first activation, node $A$'s influence $I$ can be expressed as a proportion
$$I = \frac{E_{A}}{E_{total}} \times 100$$
where $E_A$ is the energy node $A$ had contributed and $E_{total}$ is the total amount of energy node $B$ had recieved for the first activation. But then I got stuck on multiple activations.
I am unsure on how to get node $A$'s overall influence while taking into account the number of times node $B$ had activated.
My Method
So as a solution, I thought of treating each activation as its own event and using the previous formula as a partial influence $P_{n}$ for the nth activation
$$P_{n} = \frac{E_{A\_n}}{E_{total\_n}} \times 100$$
where $E_{A\_n}$ is the energy node $A$ had contributed for the nth activation and $E_{total\_n}$ is the total amount of energy node $B$ had recieved for the nth activation.
I then average the partial influences for the overall influence $O$
$$O = \frac{\sum_{\ n} P_{n}}{\#\ of\ A_{ctivations}} \ .$$
However, I am unsure that this method accurately represents what I need and suspect that my logic may be flawed.
Question
What function will determine the overall influence node $A$ had over node $B$'s actions? Is my reasoning correct or does it contain potholes?
If your function requires other variables not included in this question (such as number of input nodes or threshold value), please state what they represent. Thank you for your help!