Related papers: On $G^p$-unimodality of radius functions in graphs…

For an ordered subset $W = \{w_1, w_2,\dots w_k\}$ of vertices and a vertex $u$ in a connected graph $G$, the representation of $u$ with respect to $W$ is the ordered $k$-tuple $ r(u|W)=(d(v,w_1), d(v,w_2),\dots,$ $d(v,w_k))$, where…

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…

Random spatial networks-that is, graphs whose connectivity is governed by geometric proximity-have emerged as fundamental models for systems constrained by an underlying spatial structure. A prototypical example is the random geometric…

A $c$-labeling $\phi: V(G) \rightarrow \{1, 2, \hdots, c \}$ of graph $G$ is distinguishing if, for every non-trivial automorphism $\pi$ of $G$, there is some vertex $v$ so that $\phi(v) \neq \phi(\pi(v))$. The distinguishing number of $G$,…

Extremal graph theory studies the maximum or minimum number of subgraphs isomorphic to a prescribed graph under given constraints. \textit{Localization} has recently emerged as a framework that refines such problems by assigning extremal…

Recently there has been increased interest in fitting generative graph models to real-world networks. In particular, Bl\"asius et al. have proposed a framework for systematic evaluation of the expressivity of random graph models. We extend…

In this survey, we explore recent literature on finding the cores of higher graphs using geometric and topological means. We study graphs, hypergraphs, and simplicial complexes, all of which are models of higher graphs. We study the notion…

Learning discriminative node representations benefits various downstream tasks in graph analysis such as community detection and node classification. Existing graph representation learning methods (e.g., based on random walk and contrastive…

One of the most useful measures of cluster quality is the modularity of a partition, which measures the difference between the number of the edges joining vertices from the same cluster and the expected number of such edges in a random…

The study of vertex centrality measures is a key aspect of network analysis. Naturally, such centrality measures have been generalized to groups of vertices; for popular measures it was shown that the problem of finding the most central…

Shortest path graph distances are widely used in data science and machine learning, since they can approximate the underlying geodesic distance on the data manifold. However, the shortest path distance is highly sensitive to the addition of…

This paper studies the problem of matching two complete graphs with edge weights correlated through latent geometries, extending a recent line of research on random graph matching with independent edge weights to geometric models.…

We study the problem of \emph{local search} on a graph. Given a real-valued black-box function f on the graph's vertices, this is the problem of determining a local minimum of f--a vertex v for which f(v) is no more than f evaluated at any…

Graph machine learning architectures are typically tailored to specific tasks on specific datasets, which hinders their broader applicability. This has led to a new quest in graph machine learning: how to build graph foundation models…

For graphs $G$ and $H$, a homomorphism from $G$ to $H$ is a function $\varphi \colon V(G) \to V(H)$, which maps vertices adjacent in $G$ to adjacent vertices of $H$. A homomorphism is locally injective if no two vertices with a common…

The complexity of graph homomorphisms has been a subject of intense study [11, 12, 4, 42, 21, 17, 6, 20]. The partition function $Z_{\mathbf A}(\cdot)$ of graph homomorphism is defined by a symmetric matrix $\mathbf A$ over $\mathbb C$. We…

A set is called r-independent, if every two vertices of it are in distance greater then r. In the r-independent set problem with parameter k, we ask whether in a given graph G there exists an r-independent set of size k. In this work we…

We consider the $\Pi$-free Deletion problem parameterized by the size of a vertex cover, for a range of graph properties $\Pi$. Given an input graph $G$, this problem asks whether there is a subset of at most $k$ vertices whose removal…

For a fixed finite collection of graphs ${\cal F}$, the ${\cal F}$-M-DELETION problem asks, given an $n$-vertex input graph $G,$ for the minimum number of vertices that intersect all minor models in $G$ of the graphs in ${\cal F}$. by…

The functional graph of a function $g:X\rightarrow X$ is the directed graph with vertex set $X$ the edges of which are of the form $x\rightarrow g(x)$ for $x\in X$. Functional graphs are heavily studied because they allow one to understand…