A Linear Algorithm for Finding the Invariant Edges of an Edge-Weighted Graph

Given an edge-weighted graph where all weights are nonnegative reals, an edge reweighting is an assignment of nonnegative reals to edges such that, for each vertex, the sums of given and new weights assigned to the edges incident on the vertex do coincide. An edge is then said to be invariant if its weight is the same for any edge reweighting. We show that the set of invariant edges of an arbitrary edge-weighted graph can be determined in time linear in the size of the underlying graph. Moreover, an application to the security of statistical data is discussed. Key words. linear algebra, graph algorithms, matroid theory AMS subject classifications. 05B35, 05C50, 15A03, 62Q05, 68R10 PII. S0097539700376068

• Type: Journal
• Year: 2002
• Where: SIAMCOMP
• Authors: Francesco M. Malvestuto, Mauro Mezzini
• Keywords: Arbitrary Edge-weighted Graph, Edge-weighted Graph, Nonnegative Reals, SIAMCOMP 2002