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The operability of a network concerns its ability to remain operational, despite possible failures in its links or equipment. One may model the network through a graph to evaluate and increase this operability. Its vertices and edges…
Research on the vulnerability of electric networks with a complex network approach has produced significant results in the last decade, especially for transmission networks. These studies have shown that there are causal relations between…
Let $\Lambda(T)$ denote the set of leaves in a tree $T$. One natural problem is to look for a spanning tree $T$ of a given graph $G$ such that $\Lambda(T)$ is as large as possible. This problem is called maximum leaf number, and it is a…
Robustness against adversarial attack in neural networks is an important research topic in the machine learning community. We observe one major source of vulnerability of neural nets is from overparameterized fully-connected layers. In this…
Deep neural networks have achieved impressive performance on a variety of tasks, but their brittleness to distributional shifts remains a significant barrier to real-world deployment. In this paper, we propose a framework to analyse and…
Rapid reliability assessment of transportation networks can enhance preparedness, risk mitigation, and response management procedures related to these systems. Network reliability analysis commonly considers network-level performance and…
While many approaches to make neural networks more fathomable have been proposed, they are restricted to interrogating the network with input data. Measures for characterizing and monitoring structural properties, however, have not been…
Efforts in the recommendation community are shifting from the sole emphasis on utility to considering beyond-utility factors, such as fairness and robustness. Robustness of recommendation models is typically linked to their ability to…
Vertex similarity is a major problem in network science with a wide range of applications. In this work we provide novel perspectives on finding (dis)similar vertices within a network and across two networks with the same number of vertices…
Much of the past work in network analysis has focused on analyzing discrete graphs, where binary edges represent the "presence" or "absence" of a relationship. Since traditional network measures (e.g., betweenness centrality) utilize a…
We propose a complexity measure which addresses the functional flexibility of networks. It is conjectured that the functional flexibility is reflected in the topological diversity of the assigned graphs, resulting from a resolution of their…
We develop a theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes. Our approach generalizes the usual (co)variance to the setting of…
There are several metrics (Modularity, Mutual Information, Conductance, etc.) to evaluate the strength of graph clustering in large graphs. These metrics have great significance to measure the effectiveness and they are often used to find…
The success of graph embeddings or node representation learning in a variety of downstream tasks, such as node classification, link prediction, and recommendation systems, has led to their popularity in recent years. Representation learning…
In the problem of structured prediction with graph representation learning (GRL for short), the hypothesis returned by the algorithm maps the set of features in the \emph{receptive field} of the targeted vertex to its label. To understand…
We perform the first adversarial robustness study into Graph Neural Networks (GNNs) that are provably more powerful than traditional Message Passing Neural Networks (MPNNs). In particular, we use adversarial robustness as a tool to uncover…
The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of…
Whether as telecommunications or power systems, networks are very important in everyday life. Maintaining these networks properly functional and connected, even under attacks or failures, is of special concern. This topic has been…
Graph condensation (GC) has gained significant attention for its ability to synthesize smaller yet informative graphs. However, existing studies often overlook the robustness of GC in scenarios where the original graph is corrupted. In such…
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…