Autism spectrum disorder (ASD) is theoretically characterized by alterations in functional connectivity between brain regions. Many works presented approaches to determine informative patterns that help to predict autism from typical development. However, most of the proposed pipelines are not specifically designed for the autism problem, i.e they do not corroborate with autism theories about functional connectivity. In this paper, we propose a framework that takes into account the properties of local connectivity and long range under-connectivity in the autistic brain. The originality of the proposed approach is to adopt elimination as a technique in order to well emerge the autistic brain connectivity alterations, and show how they contribute to differentiate ASD from controls. Experimental results conducted on the large multi-site Autism Brain Imaging Data Exchange (ABIDE) show that our approach provides accurate prediction up to 70% and succeeds to prove the existence of deficits in the long-range connectivity in the ASD subjects brains.