Crumpled sheets of paper tend to exhibit specific and complex structure, which is usually described as ridge network by physicists. Existing literature has showed that it is difficult to automate ridge network detection in crumpled paper because of its complex structure. In this paper, we attempt to develop an automatic detection process in terms of our proposed density criterion. We model the ridge network as a weighted graph, where the nodes indicate the intersections of ridges and the edges are the straightened ridges detected in crumpled paper. We construct the weighted graph by first detecting the nodes and then determining the edge weight using the ridge responses. Next, we formulate a graph density criterion to evaluate the detected ridge network. Finally, we propose an edge linking method to construct the graph by maximizing the proposed density criterion. Our experimental results show that, with the density criterion, our proposed node detection together with the edge line linking method could effectively automate the ridge network detection.