Shengmin Jin

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Electrical Engineering and Computer Science


Zafarani, Reza


Graph Mining, Machine Learning on Graphs, Network Representation, Spectral Graphs

Subject Categories

Computer Sciences | Physical Sciences and Mathematics


Networks (or interchangeably graphs) have been ubiquitous across the globe and within science and engineering: social networks, collaboration networks, protein-protein interaction networks, infrastructure networks, among many others. Machine learning on graphs, especially network representation learning, has shown remarkable performance in network-based applications, such as node/graph classification, graph clustering, and link prediction. Like performance, it is equally crucial for individuals to understand the behavior of machine learning models and be able to explain how these models arrive at a certain decision. Such needs have motivated many studies on interpretability in machine learning. For example, for social network analysis, we may need to know the reasons why certain users (or groups) are classified or clustered together by the machine learning models, or why a friend recommendation system considers some users similar so that they are recommended to connect with each other. Therefore, an interpretable network representation is necessary and it should carry the graph information to a level understandable by humans.

Here, we first introduce our method on interpretable network representations: the network shape. It provides a framework to represent a network with a 3-dimensional shape, and one can customize network shapes for their need, by choosing various graph sampling methods, 3D network embedding methods and shape-fitting methods. In this thesis, we introduce the two types of network shape: a Kronecker hull which represents a network as a 3D convex polyhedron using stochastic Kronecker graphs as the network embedding method, and a Spectral Path which represents a network as a 3D path connecting the spectral moments of the network and its subgraphs.

We demonstrate that network shapes can capture various properties of not only the network, but also its subgraphs. For instance, they can provide the distribution of subgraphs within a network, e.g., what proportion of subgraphs are structurally similar to the whole network? Network shapes are interpretable on different levels, so one can quickly understand the structural properties of a network and its subgraphs by its network shape. Using experiments on real-world networks, we demonstrate that network shapes can be used in various applications, including (1) network visualization, the most intuitive way for users to understand a graph; (2) network categorization (e.g., is this a social or a biological network?); (3) computing similarity between two graphs. Moreover, we utilize network shapes to extend biometrics studies to network data, by solving two problems: network identification (Given an anonymized graph, can we identify the network from which it is collected? i.e., answering questions such as ``where is this anonymized graph sampled from, Twitter or Facebook?") and network authentication (If one claims the graph is sampled from a certain network, can we verify this claim?). The overall objective of the thesis is to provide a compact, interpretable, visualizable, comparable and efficient representation of networks.


Open Access