This paper presents a new two-stage hypergraph-based algorithm for edge detection in noise-free gray images. The first stage consists of mapping the input image onto a hypergraph called the Intensity Interval Hypergraph (IIHG) associated with the image. In the second stage, each hyperedge is partitioned into two disjoint subsets, namely, the interior pixels and the edge pixels. The interior pixels are then suppressed, so that the edge pixels trace out the edges in the image. These edges are then sharpened using an edge sharpener function to eliminate all the duplicated edges. The algorithm is validated on a number of images of largely varying details, and shows promising results. Other hypergraph-based algorithms are of computational complexity O (n2) or O (n3) whereas the IIHG model works at a reduced computational complexity of O (n).