Related papers: Supermodularity in Unweighted Graph Opitimization …
Constructions of directed configuration graphs based on a given bi-degree distribution were introduced in random graph theory some years ago. These constructions lead to graphs where the degrees of two nodes belonging to the same edge are…
Most real-world networks are weighted graphs with the weight of the edges reflecting the relative importance of the connections. In this work, we study non degree dependent correlations between edge weights, generalizing thus the…
We introduce a generalization of the zig-zag product of regular digraphs (directed graphs), which allows us to construct regular digraphs with m ore flexible choices of the degrees. In our generalization, we can control the connectivity of…
In this paper, we present enumeration algorithms to list all preferred extensions of an argumentation framework. This task is equivalent to enumerating all maximal semikernels of a directed graph. For directed graphs on $n$ vertices, all…
Clustering is an important topic in algorithms, and has a number of applications in machine learning, computer vision, statistics, and several other research disciplines. Traditional objectives of graph clustering are to find clusters with…
Network topology plays a key role in many phenomena, from the spreading of diseases to that of financial crises. Whenever the whole structure of a network is unknown, one must resort to reconstruction methods that identify the least biased…
Neighborhood graphs are a critical but often fragile step in spectral clustering of text embeddings. On realistic text datasets, standard $k$-NN graphs can contain many disconnected components at practical sparsity levels (small $k$),…
The isomorphism problem for planar graphs is known to be efficiently solvable. For planar 3-connected graphs, the isomorphism problem can be solved by efficient parallel algorithms, it is in the class $AC^1$. In this paper we improve the…
Counting linear extensions is a fundamental problem in poset theory. It is known to be #P-complete, with polynomial-time formulas available in special cases. In this work, we develop new recursive formulas for counting linear extensions of…
We explore pseudometrics for directed graphs in order to better understand their topological properties. The directed flag complex associated to a directed graph provides a useful bridge between network science and topology. Indeed, it has…
Previous hypergraph expansions are solely carried out on either vertex level or hyperedge level, thereby missing the symmetric nature of data co-occurrence, and resulting in information loss. To address the problem, this paper treats…
Given two classes of graphs, $\mathcal{G}_1\subseteq \mathcal{G}_2$, and a $c$-connected graph $G\in \mathcal{G}_1$, we wish to augment $G$ with a smallest cardinality set of new edges $F$ to obtain a $k$-connected graph $G'=(V,E\cup F) \in…
In some applications of matching, the structural or hierarchical properties of the two graphs being aligned must be maintained. The hierarchical properties are induced by the direction of the edges in the two directed graphs. These…
Given a simple connected graph on $N$ vertices with size $|E|$ and degree sequence $d_{1}\leq d_{2}\leq ...\leq d_{N}$, the aim of this paper is to exhibit new upper and lower bounds for the additive degree-Kirchhoff index in closed forms,…
Given an underlying undirected simple graph, we consider the set of all acyclic orientations of its edges. Each of these orientations induces a partial order on the vertices of our graph and, therefore, we can count the number of linear…
In this paper, we present an on-line fully dynamic algorithm for maintaining strongly connected component of a directed graph in a shared memory architecture. The edges and vertices are added or deleted concurrently by fixed number of…
This paper aims to maximize algebraic connectivity of networks via topology design under the presence of constraints and an adversary. We are concerned with three problems. First, we formulate the concave maximization topology design…
Conventional spectral digraph partitioning methods typically symmetrize the adjacency matrix, thereby transforming the directed graph partitioning problem into an undirected one, where bipartitioning is commonly linked to minimizing graph…
Boesch and Chen (SIAM J. Appl. Math., 1978) introduced the cut-version of the generalized edge-connectivity, named $k$-edge-connectivity. For any integer $k$ with $2\leq k\leq n$, the {\em $k$-edge-connectivity} of a graph $G$, denoted by…
We describe two efficient on-line algorithms to simplify weighted graphs by eliminating degree-two vertices. Our algorithms are on-line in that they react to updates on the data, keeping the simplification up-to-date. The supported updates…