Iterated Line Graph Neural Networks

A line graph transforms a graph by turning each edge into a vertex, with two such vertices adjacent exactly when the corresponding edges in the original graph share an endpoint. An iterated line graph is obtained by repeatedly applying this construction: starting from L 0 (G) = G, one defines L k+1 (G) = L(L k (G)), thereby generating a hierarchy of graphs that encodes higher-order edge-incidence structure. Line Graph Neural Networks exploit this viewpoint by propagating representations over both nodes and edges via message passing on the (oriented) line-graph adjacency. In this paper, we introduce a new architecture, Iterated Line Graph Neural Networks, and examine its fundamental properties.