Before revision:  However, most graph data , even the data with hierarchical structures are not trees and they usually do not ubiquitously match the constant curvature property of the hyperbolic space.
After revision:  However, many real-world hierarchically structured data such as taxonomies and multitree networks have varying local structures and they are not trees and they usually do not ubiquitously match the constant curvature property of the hyperbolic space.