# Subgraph Networks with Application to Structural Feature Space Expansion

## TL;DR

This paper introduces subgraph networks (SGNs) to expand the structural feature space of real-world networks, improving network classification accuracy by leveraging hierarchical subgraph structures.

## Contribution

The paper proposes a novel concept of subgraph networks and algorithms for constructing first- and second-order SGNs to enhance network feature representation.

## Key findings

- SGNs improve network classification performance
- SGNs complement original network features
- Higher-order SGNs can be extended from first- and second-order ones

## Abstract

Real-world networks exhibit prominent hierarchical and modular structures, with various subgraphs as building blocks. Most existing studies simply consider distinct subgraphs as motifs and use only their numbers to characterize the underlying network. Although such statistics can be used to describe a network model, or even to design some network algorithms, the role of subgraphs in such applications can be further explored so as to improve the results. In this paper, the concept of subgraph network (SGN) is introduced and then applied to network models, with algorithms designed for constructing the 1st-order and 2nd-order SGNs, which can be easily extended to build higher-order ones. Furthermore, these SGNs are used to expand the structural feature space of the underlying network, beneficial for network classification. Numerical experiments demonstrate that the network classification model based on the structural features of the original network together with the 1st-order and 2nd-order SGNs always performs the best as compared to the models based only on one or two of such networks. In other words, the structural features of SGNs can complement that of the original network for better network classification, regardless of the feature extraction method used, such as the handcrafted, network embedding and kernel-based methods.