  Any kind of network can be naturally represented by a Directed Acyclic Graph
(DAG); additionally, activation functions can determine the reaction of each
node of the network with respect to the signal(s) incoming. We study the
characterization of the signal distribution in a network under the lens of
tensor algebra. More specifically, we describe every activation function as
tensor distributions with respect to the nodes, called \textit{activation
tensors}. The distribution of the signal is encoded in the \textit{total
tensor} of the network. We formally prove that the total tensor can be obtained
by computing the \textit{Batthacharya-Mesner Product} (BMP), an $n$-ary
operation for tensors of order $n$, on the set of the activation tensors
properly ordered and processed via two basic operations, that we call
\textit{blow} and \textit{forget}. Our theoretical framework can be validated
through the related code developed in Python.
