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Based on the previously proposed concept Understanding Tree, this paper introduces two concepts: Understanding Graph and Understanding Map, and explores their potential applications. Understanding Graph and Understanding Map can be deemed…
Graph-based anomaly detection is pivotal in diverse security applications, such as fraud detection in transaction networks and intrusion detection for network traffic. Standard approaches, including Graph Neural Networks (GNNs), often…
Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…
In reliable decision-making systems based on machine learning, models have to be robust to distributional shifts or provide the uncertainty of their predictions. In node-level problems of graph learning, distributional shifts can be…
The connectivity structure of graphs is typically related to the attributes of the nodes. In social networks for example, the probability of a friendship between two people depends on their attributes, such as their age, address, and…
Similarity search is a fundamental task for exploiting information in various applications dealing with graph data, such as citation networks or knowledge graphs. While this task has been intensively approached from heuristics to graph…
Can we learn more from data than existed in the generating process itself? Can new and useful information be constructed from merely applying deterministic transformations to existing data? Can the learnable content in data be evaluated…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
Different from the current node-level anomaly detection task, the goal of graph-level anomaly detection is to find abnormal graphs that significantly differ from others in a graph set. Due to the scarcity of research on the work of…
For certain groups, parabolic subgroups appear as stabilizers of flags of sets or vector spaces. Quotients by these parabolic subgroups represent orbits of flags, and their cardinalities asymptotically reveal entropies (as rates of…
Introduced the quantitative measure of the structural complexity of the graph (complex network, etc.) based on a procedure similar to the renormalization process, considering the difference between actual and averaged graph structures on…
Large knowledge graphs combine human knowledge garnered from projects ranging from academia and institutions to enterprises and crowdsourcing. Within such graphs, each relationship between two nodes represents a basic fact involving these…
Entropy is a classical measure to quantify the amount of information or complexity of a system. Various entropy-based measures such as functional and spectral entropies have been proposed in brain network analysis. However, they are less…
Graph neural networks (GNNs) demonstrate a robust capability for representation learning on graphs with complex structures, showcasing superior performance in various applications. The majority of existing GNNs employ a graph convolution…
The graph entropy describes the structural information of graph. Motivated by the definition of graph entropy in general graphs, the graph entropy of hypergraphs based on Laplacian degree are defined. Some results on graph entropy of simple…
The container methods are powerful tools to bound the number of independent sets of graphs and hypergraphs, and they have been extremely influential in the area of extremal and probabilistic combinatorics. We will focus on more specialized…
Memory is an important cognitive function for humans. How a brain with such a small power can complete such a complex memory function, the working mechanism behind this is undoubtedly fascinating. Engram theory views memory as the…
The intricate relations between elements in natural and human-made systems sustain the complex processes that shape our world, forming multiscale networks of interactions. These networks can be represented as graphs composed of nodes…
Graph isomorphism is a problem for which there is no known polynomial-time solution. Nevertheless, assessing (dis)similarity between two or more networks is a key task in many areas, such as image recognition, biology, chemistry, computer…
The degree-based entropy of a graph is defined as the Shannon entropy based on the information functional that associates the vertices of the graph with the corresponding degrees. In this paper, we study extremal problems of finding the…