Graph with repeated/redundant edges?
Graphs, as usually defined, don't have parallel edges. Graphs with parallel edges are known as multigraphs.

However, like humpty dumpty, we can give a term whatever meaning we want. In some contexts, all graphs are multigraphs, and so the word graph denotes a multigraph. In other contexts, there are graphs and graphs with parallel edges. In yet other contexts, there are graphs and multigraphs. Only you know the conventions in your field.