ILIGRA: An Efficient Inverse Line Graph Algorithm

This paper presents a new and efficient algorithm, ILIGRA, for inverse line graph construction. Given a line graph H, ILIGRA constructs its root graph G with the time complexity being linear in the number of nodes in H. If ILIGRA does not know whether the given graph H is a line graph, it firstly assumes that H is a line graph and starts its...

Random line graphs and a linear law for assortativity

For a fixed number N of nodes, the number of links L in the line graph H(N,L) can only appear in consecutive intervals, called a band of L. We prove that some consecutive integers can never represent the number of links L in H(N,L), and they are called a bandgap of L. We give the exact expressions of bands and bandgaps of L. We propose a model...