Related papers: Analyzing Network Robustness via Residual Closenes…
Metros (heavy rail transit systems) are integral parts of urban transportation systems. Failures in their operations can have serious impacts on urban mobility, and measuring their robustness is therefore critical. Moreover, as physical…
Redundancy needs more precise characterization as it is a major factor in the evolution and robustness of networks of multivariate interactions. We investigate the complexity of such interactions by inferring a connection transitivity that…
It has been recently proposed that the natural connectivity can be used to characterize efficiently the robustness of complex networks. The natural connectivity quantifies the redundancy of alternative routes in the network by evaluating…
Graphs are pervasive in our everyday lives, with relevance to biology, the internet, and infrastructure, as well as numerous other applications. It is thus necessary to have an understanding as to how quickly a graph disintegrates, whether…
Graph Neural Networks (GNNs) are neural models that leverage the dependency structure in graphical data via message passing among the graph nodes. GNNs have emerged as pivotal architectures in analyzing graph-structured data, and their…
Recent work on the internet, social networks, and the power grid has addressed the resilience of these networks to either random or targeted deletion of network nodes. Such deletions include, for example, the failure of internet routers or…
Understanding and characterizing the vulnerability of urban infrastructures, which refers to the engineering facilities essential for the regular running of cities and that exist naturally in the form of networks, is of great value to us.…
Graph neural networks (GNNs) are an emerging model for learning graph embeddings and making predictions on graph structured data. However, robustness of graph neural networks is not yet well-understood. In this work, we focus on node…
Just as a herd of animals relies on its robust social structure to survive in the wild, similarly robustness is a crucial characteristic for the survival of a complex network under attack. The capacity to measure robustness in complex…
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…
A crucial challenge in network theory is the study of the robustness of a network after facing a sequence of failures. In this work, we propose a dynamical definition of network's robustness based on Information Theory, that considers…
The weak minor G of a graph G is the graph obtained from G by a sequence of edge-contraction operations on G. A weak-minor-closed family of upper embeddable graphs is a set G of upper embeddable graphs that for each graph G in G, every weak…
A graph neural network transforms features in each vertex's neighborhood into a vector representation of the vertex. Afterward, each vertex's representation is used independently for predicting its label. This standard pipeline implicitly…
We perform a massive evaluation of neural networks with architectures corresponding to random graphs of various types. We investigate various structural and numerical properties of the graphs in relation to neural network test accuracy. We…
Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…
We explore the rigidity of generic frameworks in 3-dimensions whose underlying graph is close to being planar. Specifically we consider apex graphs, edge-apex graphs and their variants and prove independence results in the generic…
Vertex classification -- the problem of identifying the class labels of nodes in a graph -- has applicability in a wide variety of domains. Examples include classifying subject areas of papers in citation networks or roles of machines in a…
There are several centrality measures that have been introduced and studied for real world networks. They account for the different vertex characteristics that permit them to be ranked in order of importance in the network. Betweenness…
Graph is a fundamental mathematical structure in characterizing relations between different objects and has been widely used on various learning tasks. Most methods implicitly assume a given graph to be accurate and complete. However, real…
Neural networks are often represented as graphs of connections between neurons. However, despite their wide use, there is currently little understanding of the relationship between the graph structure of the neural network and its…