A chord diagram is a circle with chords going across it connecting 2 points on the boundary. You can associate to a chord diagram a graph with vertices representing the chords and an edge between them if the chords intersect in the chord diagram, called the intersection graph. A question is "If 2 chord diagrams have the same graph are they equal in the algebra of chord diagrams?" The answer is yes for graphs that are trees and ones containing a single loop. I will go in depth about these cases in my talk and also show 2 related art pieces.