Searching for high-dimensional vector data with high accuracy is an inevitable search technology for various types of data. Graph-based indexes are known to reduce the query time for high-dimensional data. To further improve the query time by using graphs, we focused on the indegrees and outdegrees of graphs. While a sufficient number of incoming edges (indegrees) are indispensable for increasing search accuracy, an excessive number of outgoing edges (outdegrees) should be suppressed so as to not increase the query time. Therefore, we propose three degree-adjustment methods: static degree adjustment of not only outdegrees but also indegrees, dynamic degree adjustment with which outdegrees are determined by the search accuracy users require, and path adjustment to remove edges that have alternative search paths to reduce outdegrees. We also show how to obtain optimal degree-adjustment parameters and that our methods outperformed previous methods for image and textual data.