A graphoidal cover of a graph $G$ is a collection $\\psi$ of (not necessarily open) paths in $G$ such that every path in $\\psi$ has at least two vertices, every vertex of $G$ is an internal vertex of at most one path in $\\psi$, every edge of $G$ is in exactly one path in $\\psi$. The minimum cardinality of a graphoidal cover of $G$ is called the graphoidal covering number of $G$ and is denoted by $\\eta(G)$ or $\\eta$. In this paper, we have obtained the graphoidal covering number for the class of graphs $G \\not \\in \\mathcal{F}$ through their edge connectivity.