Network graphs are common visualization charts. They often appear in the form of bitmaps in articles, web pages, magazine prints, and designer sketches. People often want to modify graphs because of their poor design, but it is difficult to obtain their underlying data. In this article, we present VividGraph, a pipeline for automatically extracting and redesigning graphs from static images. We propose using convolutional neural networks to solve the problem of graph data extraction. Our method is robust to hand-drawn graphs, blurred graph images, and large graph images. We also present a graph classification module to make it effective for directed graphs. We propose two evaluation methods to demonstrate the effectiveness of our approach. It can be used to quickly transform designer sketches, extract underlying data from existing graphs, and interactively redesign poorly designed graphs.