[[Quiver]]
# Weight on a quiver

Let $k \in \mathbb{N}$ and $\Gamma$ be a [[quiver]] with [[adjacency matrix]] $A({\Gamma}) = (a_{ij})_{i,j=1}^r$.
A $k$-**weight** is a positive integral $k$-eigenvector of $A$, #m/def/graph 
i.e. $v_{i} \in \mathbb{N}$ such that
$$
\begin{align*}
\sum_{j=1}^r a_{ij} v_{j} = kv_{i}
\end{align*}
$$
A quiver is called $k$-**weightable** iff a $k$-weight exists.[^2021]

  [^2021]: 2021\. [[Sources/@browneConnectivityPropertiesMcKay2021|Connectivity properties of McKay quivers]]



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