  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.
