for _ in range(max_iterations):
        new_ranks = np.zeros(n)
        for page, out_links in links.items():
            if out_links:
                share = ranks[page_index[page]] / len(out_links)
                for linked_page in out_links:
                    new_ranks[page_index[linked_page]] += share
            else:
                # If a page has no out-links, it is a "dangling node"
                # We distribute its rank evenly across all pages
                new_ranks += ranks[page_index[page]] / n