Related papers: Network-Based Vertex Dissolution
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…
This work develops a flexible and mathematically sound framework for the design and analysis of graph scattering networks with variable branching ratios and generic functional calculus filters. Spectrally-agnostic stability guarantees for…
In a random linear graph, vertices are points on a line, and pairs of vertices are connected, independently, with a link probability that decreases with distance. We study the problem of reconstructing the linear embedding from the graph,…
Bipartite graphs model the relationships between two disjoint sets of entities in several applications and are naturally drawn as 2-layer graph drawings. In such drawings, the two sets of entities (vertices) are placed on two parallel lines…
We introduce the s-Plex Cluster Vertex Deletion problem. Like the Cluster Vertex Deletion problem, it is NP-hard and motivated by graph-based data clustering. While the task in Cluster Vertex Deletion is to delete vertices from a graph so…
The algorithmic differentiation (AD) of mathematical functions can be interpreted as a sequence of vertex eliminations in an underlying directed acyclic graph. The problem of determining a minimum-cost elimination ordering, which we call…
Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…
The sensitivity of networks regarding the removal of vertices has been studied extensively within the last 15 years. A common approach to measure this sensitivity is (i) removing successively vertices by following a specific removal…
Exchangeable models for countable vertex-labeled graphs cannot replicate the large sample behaviors of sparsity and power law degree distribution observed in many network datasets. Out of this mathematical impossibility emerges the question…
A graph vertex-subset problem defines which subsets of the vertices of an input graph are feasible solutions. We view a feasible solution as a set of tokens placed on the vertices of the graph. A reconfiguration variant of a vertex-subset…
Natural physical, chemical, and biological dynamical systems are often complex, with heterogeneous components interacting in diverse ways. We show how simple graph neural networks can be designed to jointly learn the interaction rules and…
Document structure analysis, such as zone segmentation and table recognition, is a complex problem in document processing and is an active area of research. The recent success of deep learning in solving various computer vision and machine…
Consider a network that evolves according to a reversible, nearest neighbours dynamics. Is the dynamics allowed to vary the size of the network? On the one hand it seems that, being the principal carriers of information, nodes cannot be…
As the scale of networked control systems increases and interactions between different subsystems become more sophisticated, questions of the resilience of such networks increase in importance. The need to redefine classical system and…
Finding the set of nodes, which removed or (de)activated can stop the spread of (dis)information, contain an epidemic or disrupt the functioning of a corrupt/criminal organization is still one of the key challenges in network science. In…
Deciding whether a political districting plan was distorted by a hidden agenda, or whether it dilutes the voting power of some group, requires a neutral baseline for comparison. Remarkably, all nine U.S. Supreme Court justices have now…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
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…
Graph burning is a simple model for the spread of social influence in networks. The objective is to measure how quickly a fire (e.g., a piece of fake news) can be spread in a network. The burning process takes place in discrete rounds. In…
Given a finite undirected graph $X$, a vertex is $0$-dismantlable if its open neighbourhood is a cone and $X$ is $0$-dismantlable if it is reducible to a single vertex by successive deletions of $0$-dismantlable vertices. By an iterative…