page 15 : modular-width – The modular-width $mw(G)$ of a graph $G$ is the smallest number $h$ such that a $k$-partition $(V_1,\dots,V_k)$ of $G$ exists, where $k \le h$ and each subset $V_i$, $i \in [k]$ is a module and either contains a single vertex or for which the modular-subgraph $G[V_i]$ has a modular-width of $h$.
page 25 : bounded path does not imply bounded modular-width – The Modular-width of a path $P$ with length $n > 3$ is $n$.