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The index-permutation graph (IPG) model is a natural extension of the Cayley graph model, and super-IPGs form an efficient class of IPGs that contain a wide variety of networks as subclasses. In this paper, we derive a number of efficient algorithms and embeddings for super-IPGs, proving their versatility. We show that a multitude of important networks can also be emulated in super-IPGs with optimal slowdown. Also, the intercluster diameter average intercluster distance, and bisection bandwidth of suitably constructed super-IPGs are optimal within small constant factors. Finally we show that when parallel computers, built as multiple chip-multiprocessors (MCMP), are based on super-IPGs, they can significantly outperform those based on hypercubes, k-ary n-cubes, and other networks in carrying out communication-intensive tasks.