Related papers: Finding HeavyPaths in Weighted Graphs and a Case-S…
A hypergraph is a set V of vertices and a set of non-empty subsets of V, called hyperedges. Unlike graphs, hypergraphs can capture higher-order interactions in social and communication networks that go beyond a simple union of pairwise…
We consider the task of drawing a graph on multiple horizontal layers, where each node is assigned a layer, and each edge connects nodes of different layers. Known algorithms determine the orders of nodes on each layer to minimize crossings…
Community detection, aiming to group the graph nodes into clusters with dense inner-connection, is a fundamental graph mining task. Recently, it has been studied on the heterogeneous graph, which contains multiple types of nodes and edges,…
Let $G=(V,E,w)$ be a weighted directed graph without negative cycles. For two vertices $s,t\in V$, we let $d_{\le h}(s,t)$ be the minimum, according to the weight function $w$, of a path from $s$ to $t$ that uses at most $h$ edges, or hops.…
Many phenomena in real world social networks are interpreted as spread of influence between activated and non-activated network elements. These phenomena are formulated by combinatorial graphs, where vertices represent the elements and…
One of the defining features of complex networks is the connectivity properties that we observe emerging from local interactions. Recently, hypergraphs have emerged as a versatile tool to model networks with non-dyadic, higher-order…
An edge-ordering of a graph $G=(V,E)$ is a bijection $\phi:E\to\{1,2,...,|E|\}$. Given an edge-ordering, a sequence of edges $P=e_1,e_2,...,e_k$ is an increasing path if it is a path in $G$ which satisfies $\phi(e_i)<\phi(e_j)$ for all…
In real-world networks, predicting the weight (strength) of links is as crucial as predicting the existence of the links themselves. Previous studies have primarily used shallow graph features for link weight prediction, limiting the…
The \textit{longest path transversal number} of a connected graph $G$, denoted by $lpt(G)$, is the minimum size of a set of vertices of $G$ that intersects all longest paths in $G$. We present constant upper bounds for the longest path…
For a graph G with real weights assigned to the vertices (edges), the MAX H-SUBGRAPH problem is to find an H-subgraph of G with maximum total weight, if one exists. The all-pairs MAX H-SUBGRAPH problem is to find for every pair of vertices…
Real data collected from different applications that have additional topological structures and connection information are amenable to be represented as a weighted graph. Considering the node labeling problem, Graph Neural Networks (GNNs)…
The shortest path problem in graphs is fundamental to AI. Nearly all variants of the problem and relevant algorithms that solve them ignore edge-weight computation time and its common relation to weight uncertainty. This implies that taking…
In the information overloaded web, personalized recommender systems are essential tools to help users find most relevant information. The most heavily-used recommendation frameworks assume user interactions that are characterized by a…
The entities in directed networks arising from real-world interactions are often naturally organized under some hierarchical structure. Given a directed, weighted, graph with edges and node labels, we introduce ranking problem where the…
A graph has \emph{diameter} D if every pair of vertices are connected by a path of at most D edges. The Diameter-D Augmentation problem asks how to add the a number of edges to a graph in order to make the resulting graph have diameter D.…
A labelling of a graph is an assignment of labels to its vertex or edge sets (or both), subject to certain conditions, a well established concept. A labelling of a graph G of order n is termed a numbering when the set of integers {1,...,n}…
Finding paths in graphs is a fundamental graph-theoretic task. In this work, we we are concerned with finding a path with some constraints on its length and the number of vertices neighboring the path, that is, being outside of and incident…
We consider the Shortest Odd Path problem, where given an undirected graph $G$, a weight function on its edges, and two vertices $s$ and $t$ in $G$, the aim is to find an $(s,t)$-path with odd length and, among all such paths, of minimum…
Finding optimal paths in connected graphs requires determining the smallest total cost for traveling along the graph's edges. This problem can be solved by several classical algorithms where, usually, costs are predefined for all edges.…
Consider a random regular graph with degree $d$ and of size $n$. Assign to each edge an i.i.d. exponential random variable with mean one. In this paper we establish a precise asymptotic expression for the maximum number of edges on the…