Here are the Graph Permissions required to use Graph Search.

Please note these permissions are all delgated

DELEGATED Permissions

Note - For delegated permissions, the effective permissions of your app will be the least privileged intersection of the delegated permissions the app has been granted (through consent) and the privileges of the currently signed-in user. Your app can never have more privileges than the signed-in user. Within organizations, the privileges of the signed-in user may be determined by policy or by membership in one or more administrator roles. 

For example, assume your app has been granted the User.ReadWrite.All delegated permission in Microsoft Graph. This permission nominally grants your app permission to read and update the profile of every user in an organization. If the signed-in user is a global administrator, your app will be able to update the profile of every user in the organization. However, if the signed-in user is not in an administrator role, your app will be able to update only the profile of the signed-in user. It will not be able to update the profiles of other users in the organization because the user that it has permission to act on behalf of does not have those privileges.