In a communication network, several vulnerability measures are used to determine the resistance of the network to disruption of operation after the failure of certain stations or communication links. This study introduces a new vulnerability parameter, edge scattering number. The edge scattering number of a noncomplete connected graph $G$ is defined to be $es(G)=\max\{\omega(G-S)-|S|:S\subseteq E(G), \ \omega(G-S)>1\}$ where $\omega(G-S)$ denote the number of components in $G-S$. A set $S\subseteq E(G)$, is said to be the $es$-set of $G$, if $es(G)=\omega(G-S)-|S|$. In this paper contains results on bounds for the edge scattering number. Moreover we obtain edge scattering number of some graphs.