neo4j – Graph Databases with Frontend and advanced features
There are a number of different products and approaches that can visualize big graphs from neo4j, check the link. Another one not mentioned behind that link is gephi, which is a desktop based tool but still works.
I would warn you against general force-directed layouts of a few thousand nodes at a time, because theyre rarely what you want. Generally when youre trying to visualize big graph data sets, youre going to want to think about how to lay things out differently. For example, if your dataset is temporally ordered you might be better off with a timeline than a graph. Also keep in mind that neo4j can return tabular results from cypher queries, so with a tabular result you can put that data into any existing visualization tool.
Graph visualization is a really deep topic and its hard to give a single solid answer without more on your requirements. I will say though that in data viz, usually you really just dont want to see thousands of data points, pretty much ever. When you do want to see that much data, its usually because its clustered together into clouds so that what youre really seeing is the clusters, not the points. So you might consider lumping many of your data points into clusters, and then trying to visualize THOSE rather than the raw nodes/edges.