Communication services have traditionally been characterized by high levels of service dependability. Today cable cuts, node interruptions, software errors or hardware failures and transmission failure at various points can cause interrupted service for long periods of time. Large amounts of data transmitted through fiber optic and satellite communication networks, requires greater degrees of stability or less vulnerability. The neighbour integrity is a vulnerability measure of a graph which is considered as a communications network model. This paper presents neighbour integrity of a Boolean graph. Also, theorems are given for some compounds of Boolean graphs which are obtained by using the graph operations.