Ratio-Based Distortion and Network Distance

Due to the prevalent theoretical status and high-performance efficiency in computer networks, face recognition, and heterogeneous data analysis, network distance has attracted significant attention and become an emerging technology in recent years. It is noted that the original difference-based network distance is inadequate for describing network discrepancies by proportionally expanding/contracting the weight function. To mitigate this shortcoming, this paper proposes ratio-based distortion and network distance, and defines a proportional strong/weak isomorphism which is compatible with the new setting. Several results with theoretical underpinning are deduced by means of mathematical analysis. Additionally, this paper conducts a similarity analysis experiment on a randomly generated network structure dataset using the proposed network distance formula. The analysis of the experimental results, including the corresponding hierarchical clustering diagrams and heatmaps, indicates that the proposed network distance has practical value for applications. The code and data of this paper are completely public at https://github.com/AizhEngHN/Ratio-based-distortion-and-network-distance.