Topological persistence of configuration spaces and independence complexes for digraphs

We study the topological persistence of the (path) configuration spaces and the (path) independence complexes for digraphs as well as their underlying graphs. We construct some canonical embeddings from the (path) independence complexes of the underlying graphs to the (path) independence complexes of the digraphs as well as some canonical embeddings between the (path) independence complexes induced by strong totally geodesic immersions and strong totally geodesic embeddings of (di)graphs. We apply the path homology to the path independence complexes of (di)graphs. As by-products, we derive some consequences about the Shannon capacities.