In this book authors for the first time introduce the notion of strong neutrosophic graphs. They are very different from the usual graphs and neutrosophic graphs. 

Using these new structures special subgraph topological spaces are defined. Further special lattice graph of subgraphs of these graphs are defined and described. 

Several interesting properties using subgraphs of a strong neutrosophic graph are obtained.

Several open conjectures are proposed. These new class of strong neutrosophic graphs will certainly find applications in Neutrosophic Cognitive Maps (NCM), Neutrosophic Relational Maps (NRM) and Neutrosophic Relational Equations (NRE) with appropriate modifications.