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Large time-varying graphs are increasingly common in financial, social and biological settings. Feature extraction that efficiently encodes the complex structure of sparse, multi-layered, dynamic graphs presents computational and…

The robustness of synchronization is typically characterized by scalar, per-node stability indices whose dependence on topology is studied via network science or graph neural networks (GNNs). We propose a novel upstream task, learning…

Most existing popular methods for learning graph embedding only consider fixed-order global structural features and lack structures hierarchical representation. To address this weakness, we propose a novel graph embedding algorithm named…

Including intricate topological information (e.g., cycles) provably enhances the expressivity of message-passing graph neural networks (GNNs) beyond the Weisfeiler-Leman (WL) hierarchy. Consequently, Persistent Homology (PH) methods are…

Graph learning has rapidly evolved into a critical subfield of machine learning and artificial intelligence (AI). Its development began with early graph-theoretic methods, gaining significant momentum with the advent of graph neural…

While transactions with cryptocurrencies such as Ethereum are becoming more prevalent, fraud and other criminal transactions are not uncommon. Graph analysis algorithms and machine learning techniques detect suspicious transactions that…

Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…

Determining whether two graphs are isomorphic is a fundamental problem with practical applications in areas such as molecular chemistry or social network analysis, yet it remains a challenging task, with exact solutions often being…

Ethereum relies on a peer-to-peer overlay network to propagate information. The knowledge of Ethereum network topology holds the key to understanding Ethereum's security, availability, and user anonymity. From a measurement perspective, an…

TopoDetect is a Python package that allows the user to investigate if important topological features, such as the Degree of the nodes, their Triangle Count, or their Local Clustering Score, are preserved in the embeddings of graph…

Cryptocoins (i.e., Bitcoin, Ether, Litecoin) are tradable digital assets. Ownerships of cryptocoins are registered on distributed ledgers (i.e., blockchains). Secure encryption techniques guarantee the security of the transactions…

This study proposes a credit card fraud detection method based on Heterogeneous Graph Neural Network (HGNN) to address fraud in complex transaction networks. Unlike traditional machine learning methods that rely solely on numerical features…

Network topology inference is a prominent problem in Network Science. Most graph signal processing (GSP) efforts to date assume that the underlying network is known, and then analyze how the graph's algebraic and spectral characteristics…

The consensus that GCN, GraphSAGE, GAT, and EvolveGCN outperform feature-only baselines on the Elliptic Bitcoin Dataset is widely cited but has not been rigorously stress-tested under a leakage-free evaluation protocol. We perform a…

Blockchain is rapidly emerging as an important class of network application, with a unique set of trust, security and transparency properties. In a blockchain system, participants record and update the `server-side' state of an application…

Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field.…

The concept of a blockchain has given way to the development of cryptocurrencies, enabled smart contracts, and unlocked a plethora of other disruptive technologies. But, beyond its use case in cryptocurrencies, and in network coordination…

Long lived topological features are distinguished from short lived ones (considered as topological noise) in simplicial complexes constructed from complex networks. A new topological invariant, persistent homology, is determined and…

In real-world systems, the relationships and connections between components are highly complex. Real systems are often described as networks, where nodes represent objects in the system and edges represent relationships or connections…

Hypergraph data appear and are hidden in many places in the modern age. They are data structure that can be used to model many real data examples since their structures contain information about higher order relations among data points. One…