Investigating different properties of algebraic graphs is a curious avenue of research in algebraic graph theory, as these algebraic graphs are well-structured classes of graphs. In these lines, various structural properties of the algebraic intersection graph, called the n-inordinate invariant intersection graphs, have been studied in the literature. Color connections in graphs is the assignment of colors or equivalently, labels to the entities of a non-trivial connected graph, whose protocols are defined based on the connectivity aspects. In this article, we study the different color connections in the n-inordinate invariant intersection graphs and their complements, called the n-inordinate invariant non-intersection graphs.