Render Line behind Object

I'm trying to create a graph where diamond vertices are connected by line edges. I've accomplished this by attaching a linerendererer to my vertex objects and adding the position of the vertex it should be connected to. I've attached a picture of this below. My issue is that I'd like to have the Vertices rest above the line, so once the line enters into the surface area of the vertex, it seemingly dissappears. I'm struggling to accomplish this, and feel like I'm missing something very obvious. These vertices are images on a UI canvas, what would be the best way to bring my vertices the foreground? Thanks!