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A centrality measure of the cut-edges of an undirected graph, given in [Altafini et al.~SIMAX 2023] and based on Kemeny's constant, is revisited. A numerically more stable expression is given to compute this measure, and an explicit…
In this paper, we consider the problem of assessing local clustering in complex networks. Various definitions for this measure have been proposed for the cases of networks having weighted edges, but less attention has been paid to both…
Graph representation plays an important role in the field of financial risk control, where the relationship among users can be constructed in a graph manner. In practical scenarios, the relationships between nodes in risk control tasks are…
Real-world networks often exhibit strong transitivity with nontrivial local clustering spectra and degree correlations. Such features are not easily modeled in tractable network models, creating an obstacle to the theoretical understanding…
Node clustering is a powerful tool in the analysis of networks. We introduce a graph neural network framework, named DIGRAC, to obtain node embeddings for directed networks in a self-supervised manner, including a novel probabilistic…
Graph embedding methods embed the nodes in a graph in low dimensional vector space while preserving graph topology to carry out the downstream tasks such as link prediction, node recommendation and clustering. These tasks depend on a…
Graphs and networks are used to model interactions in a variety of contexts. There is a growing need to quickly assess the characteristics of a graph in order to understand its underlying structure. Some of the most useful metrics are…
Directed graphs model asymmetric relationships between nodes and research on directed graph embedding is of great significance in downstream graph analysis and inference. Learning source and target embedding of nodes separately to preserve…
Despite the enormous success of graph neural networks (GNNs), most existing GNNs can only be applicable to undirected graphs where relationships among connected nodes are two-way symmetric (i.e., information can be passed back and forth).…
A new precoding-based intersession network coding (NC) scheme has recently been proposed, which applies the interference alignment technique, originally devised for wireless interference channels, to the 3-unicast problem of directed…
In this study, we challenge the traditional approach of frequency analysis on directed graphs, which typically relies on a single measure of signal variation such as total variation. We argue that the inherent directionality in directed…
Node classification is one of the hottest tasks in graph analysis. Though existing studies have explored various node representations in directed and undirected graphs, they have overlooked the distinctions of their capabilities to capture…
Entanglement is a complexity measure of directed graphs that origins in fixed point theory. This measure has shown its use in designing efficient algorithms to verify logical properties of transition systems. We are interested in the…
Learning the structure of causal directed acyclic graphs (DAGs) is useful in many areas of machine learning and artificial intelligence, with wide applications. However, in the high-dimensional setting, it is challenging to obtain good…
We show that prominent centrality measures in network analysis are all based on additively separable and linear treatments of statistics that capture a node's position in the network. This enables us to provide a taxonomy of centrality…
We introduce a new family of graphical models that consists of graphs with possibly directed, undirected and bidirected edges but without directed cycles. We show that these models are suitable for representing causal models with additive…
Identifying influential nodes and edges in directed networks remains a fundamental challenge across domains from social influence to biological regulation. Most existing centrality measures face a critical limitation: they either discard…
Most of the analyses concerning signed networks have focused on the balance theory, hence identifying frustration with undirected, triadic motifs having an odd number of negative edges; much less attention has been paid to their directed…
Graph minors are a primary tool in understanding the structure of undirected graphs, with many conceptual and algorithmic implications. We propose new variants of \emph{directed graph minors} and \emph{directed graph embeddings}, by…
Entanglement is a complexity measure of digraphs that origins in fixed-point logics. Its combinatorial purpose is to measure the nested depth of cycles in digraphs. We address the problem of characterizing the structure of graphs of…