Consider a graph $G=(V,E)$. Its adjacency matrix $A$ is defined by $A_{u,v} = 1$ if $(u,v)\in E$, $0$ otherwise.
Consider a vector $x$ that associates a value $x_v$ to each vertex of $G$. Consider the vector $y$ such that $y_v = \sum_{(u,v)\in E} x_u$. Then, we have $y = A\cdot x$.
Now consider a sequence of $k$ graphs $G_i = (V,E_i)$ with $i=1,2,\dots,k$. Its adjacency tensor $A$ may be defined by $A_{i,u,v} = 1$ if $(u,v) \in E_i$, $0$ otherwise.
Consider a matrix $X$ that associates a value $X_{i,v}$ to each vertex $v$ of each $G_i$. Consider the matrix $Y$ such that $Y_{i,v} = \sum_{(u,v)\in E_{i}} X_{i,v}$.
Question: Is there any way to obtain $Y$ as a product between $A$ and $X$, or any similar operation?
(Previously asked on math.stackexchange with no success.)
