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Vague graphs (VGs), belonging to the FGs family, have good capabilities when faced with problems that cannot be expressed by FGs. When an element’s membership is not clear, neutrality is a good option that can be well-supported by a VG. The previous definition limitations in irregular-FG have led us to offer new definitions in VGs. So, in this paper, we introduce the concepts of strongly edged irregular vague graphs (SEIVGs), strongly edged totally irregular vague graphs (SETIVGs), and perfectly regular vague graphs (PRVGs) with several examples. A comparative study between SEIVGs and SETIVGs is presented. Finally, an application of vague influence digraph has been presented.