This paper addresses the problem of the incremental con- struction of an indexing structure, namely a proximity graph, for large image collections. To this purpose, a local update strategy is examined. Considering an existing graph G and a new node q, how only a relevant sub-graph of G can be updated following the insertion of q? For a given proximity graph, we study the most recent algorithm of the literature and highlight its limitations. Then, a method that leverages an edge-based neighbourhood local update strategy to yield an approximate graph is proposed. Using real-world and synthetic data, the proposed algorithm is tested to assess the accuracy of the approximate graphs. The scalability is veried with large image collections, up to one million images.