In this book authors introduce the notion of subset vertex multigraphs for the first time. The study of subset vertex graphs was introduced in 2018, however they are not multiedged, further they were unique once the vertex subsets are given. These subset vertex multigraphs are also unique once the vertex subsets are given and the added advantage is that the number of common elements between two vertex subsets accounts for the number of edges between them, when there is no common element there is no edge between them. In case the two vertex subsets have only one common element then only one edge exists between them. When we do not associate any direction, we call them as subset vertex multigraphs of type I, when we associate direction, that is when they are directed graphs, we define them as subset vertex multigraphs of type II. If the subsets of these multigraphs are taken from the subsets of a neutrosophic set, we call them as subset vertex neutrosophic multigraphs.