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 root graph construction. During the root graph construction, ILIGRA checks whether the given graph H is a line graph and ILIGRA stops once it finds H is not a line graph. The time complexity of ILIGRA with line graph checking is linear in the number of links in the given graph H . For sparse line graphs of any size and for dense line graphs of small size, numerical results of the running time show that ILIGRA outperforms all currently available algorithms.