Related papers: A study of link graphs
The traditional complex network approach considers only the shortest paths from one node to another, not taking into account several other possible paths. This limitation is significant, for example, in urban mobility studies. In this short…
The Wiener index, $W(G)$, of a connected graph $G$ is the sum of distances between its vertices. In 2021, Akhmejanova et al. posed the problem of finding graphs $G$ with large $R_m(G)= |\{v\in V(G)\,|\,W(G)-W(G-v)=m \in \mathbb{Z} \}|/…
Graphs are a central object of study in various scientific fields, such as discrete mathematics, theoretical computer science and network science. These graphs are typically studied using combinatorial, algebraic or probabilistic methods,…
Graphs are general and powerful data representations which can model complex real-world phenomena, ranging from chemical compounds to social networks; however, effective feature extraction from graphs is not a trivial task, and much work…
We present a new, systematic approach for analyzing network topologies. We first introduce the dK-series of probability distributions specifying all degree correlations within d-sized subgraphs of a given graph G. Increasing values of d…
For a simple graph $G$, the $3$-distance graph, $D_3(G)$, is a graph with the vertex set $V(G)$ and two vertices are adjacent if and only if their distance is $3$ in the graph $G$. For a connected graph $G$, we provide some conditions for…
Link prediction requires predicting which new links are likely to appear in a graph. Being able to predict unseen links with good accuracy has important applications in several domains such as social media, security, transportation, and…
Graphs are used in almost every scientific discipline to express relations among a set of objects. Algorithms that compare graphs, and output a closeness score, or a correspondence among their nodes, are thus extremely important. Despite…
Entity-linking is a natural-language-processing task that consists in identifying the entities mentioned in a piece of text, linking each to an appropriate item in some knowledge base; when the knowledge base is Wikipedia, the problem comes…
Unigraphs are graphs identifiable up to isomorphism from their degree sequences. Given a class $\mathcal{A}$ of graphs, we define the class of $\mathcal{A}$-unigraphs to be graphs identifiable from degree sequence and membership in…
Given a graph $G$, the (graph theory) general position problem is to find the maximum number of vertices such that no three vertices lie on a common geodesic. This graph invariant is called the general position number (gp-number for short)…
An \emph{s-graph} is a graph with two kinds of edges: \emph{subdivisible} edges and \emph{real} edges. A \emph{realisation} of an s-graph $B$ is any graph obtained by subdividing subdivisible edges of $B$ into paths of arbitrary length (at…
We introduce the tree distance, a new distance measure on graphs. The tree distance can be computed in polynomial time with standard methods from convex optimization. It is based on the notion of fractional isomorphism, a characterization…
We consider the NP-complete problem of tracking paths in a graph, first introduced by Banik et. al. [3]. Given an undirected graph with a source $s$ and a destination $t$, find the smallest subset of vertices whose intersection with any…
We address the problem of semi-supervised learning in relational networks, networks in which nodes are entities and links are the relationships or interactions between them. Typically this problem is confounded with the problem of…
A pseudoline is a homeomorphic image of the real line in the plane so that its complement is disconnected. An arrangement of pseudolines is a set of pseudolines in which every two cross exactly once. A drawing of a graph is pseudolinear if…
We introduce a dense counterpart of graph degeneracy, which extends the recently-proposed invariant symmetric difference. We say that a graph has sd-degeneracy (for symmetric-difference degeneracy) at most $d$ if it admits an elimination…
We consider the pattern detection problem in graphs: given a constant size pattern graph $H$ and a host graph $G$, determine whether $G$ contains a subgraph isomorphic to $H$. Our main results are: * We prove that if a pattern $H$ contains…
A graph G is an NG-graph if \chi(G) + \chi(G complement) = |V(G)| + 1. We characterize NG-graphs solely from degree sequences leading to a linear-time recognition algorithm. We also explore the connections between NG-graphs and split…
The study of graph queries in database theory has spanned more than three decades, resulting in a multitude of proposals for graph query languages. These languages differ in the mechanisms. We can identify three main families of languages,…