An Equation Involving the Neighborhood (Two-Step) and Line Graphs.
Mary M. Miller, Robert C. Brigham, Ronald D. Dutton · Journal of International Crisis and Risk Communication Research · 1999
The neighborhood or two-step graph, N(G), of a graph G is the intersection graph of the open neighborhoods of the vertices of G, and L(G) is the line graph of G. The class of graphs for which N[L(G)] ≅ L[N(G)] consists of those graphs for which every component is either K1, K1,3, or Cn where n ≥ 3 and n ≠ 4.