The effect of collaborators on institutions scientific impact was examined for 81 institutions with different degrees of impact and collaboration. Not only collaborators including both core and peripheral collaborators cite each other more than non-collaborators, but also the first group cites each other faster than the second group even when self-citations were ignored. Although high impact institutions and more collaborative institutions receive more citations from their collaborators, it seems that the number of these citations increases only up to a certain point. In this regard, for example, there is a slight difference between top and middle collaborative institutions; however, only a small fraction of collaborators do not cite back the papers of these two groups of institutions. The benefit of collaboration varies based on the type of collaborators, institutions, papers, citers and the publication year of cited documents. For example, the effect of collaboration decreases as the institutions level of impact increases. Hence, collaborating more does not directly imply obtaining higher impact.