Select a result to preview
To open a local graph for a given note, use the command palette to select Graph view: Open local graph.
The problem is that the default settings are suboptimal, and you have to adjust them repeatedly. There is a non-standard plugin that works very well for this. It's called "Graph Presets" and it's included in your seed vault.
When you've opened a local graph, you can Use the command palette to select Graph Presets: Apply Local Color, and the settings in the graph presets file will be applied to the local graph, and to any new graphs that you open by clicking on nodes in that graph.
By adjusting the filter settings in the graph pane, you can unlock even more powerful insights.
For information about using local graphs, as well as the graph of the full vault, see the official help page: Graph view - Obsidian Help