19 papers · ranked by Valyu relevance
László Lovász
For dense graphs, a theory that is analogous is many respects (but different in the details) is the theory of graphons. One of the important tools in graphon theory is the procedure of "purification" of a graphon, which results in a graphon that is essentially equivalent in all important properties and parameters, and…
Luís N. Baptista, James B. Kennedy, Delio Mugnolo
We introduce a natural notion of mean (or average) distance in the context of compact metric graphs, and study its relation to geometric properties of the graph. We show that it exhibits a striking number of parallels to the reciprocal of the spectral gap of the graph Laplacian with standard vertex conditions: it is…
Simone Dovetta
We investigate the existence of stationary solutions for the Nonlinear Schrödinger equation on compact metric graphs. In the L 2 -subcritical setting, we prove the existence of an infinite number of such solutions, for every value of the mass. In the critical regime, this infinity of solutions is established to exists…
Marco Düfel, James B. Kennedy, Delio Mugnolo, Marvin Plümer + 1 more
'Matthias Täufer'] Abstract. We study the interplay between spectrum, geometry and boundary conditions for two distinguished self-adjoint realisations of the Laplacian on infinite metric graphs, the so-called Friedrichs and Neumann extensions. We introduce a new criterion for compactness of the resolvent and apply this…
Aleksey Kostenko, Delio Mugnolo, Noema Nicolussi
We investigate the relationship between one of the classical notions of boundaries for infinite graphs, graph ends, and self-adjoint extensions of the minimal Kirchhoff Laplacian on a metric graph. We introduce the notion of finite volume for ends of a metric graph and show that finite volume graph ends is the proper…
Rion Brattig Correia, Alain Barrat, Luis M. Rocha
The structure of social networks strongly affects how different phenomena spread in human society, from the transmission of information to the propagation of contagious diseases. It is well-known that heterogeneous connectivity strongly favors spread, but a precise characterization of the redundancy present in social…
Tatiana Lokot, Olga Abramov, Alexander Mehler, Sergio Consoli
The average geodesic distance L Newman (2003) and the compactness C*B Botafogo (1992) are important graph indices in applications of complex network theory to real-world problems. Here, for simple connected undirected graphs G of order n, we study the behavior of L(G) and C**B(G), subject to the condition that their…
Agelos Georgakopoulos
Mohar recently adapted the classical game of Cops and Robber from graphs to metric spaces, thereby unifying previously studied pursuit-evasion games. He conjectured that finitely many cops can win on any compact geodesic metric space, and that their number can be upper-bounded in terms of the ranks of the homology…
Evan DeCorte, Fernando Mário de Oliveira Filho, Frank Vallentin
We introduce the cone of completely positive functions, a subset of the cone of positive-type functions, and use it to fully characterize maximum-density distance-avoiding sets as the optimal solutions of a convex optimization problem. As a consequence of this characterization, it is possible to reprove and improve…
Tatiana Lokot, Alexander Mehler, Olga Abramov, Siamak Yassemi
In this paper, we study the limit of compactness which is a graph index originally introduced for measuring structural characteristics of hypermedia. Applying compactness to large scale small-world graphs (Mehler, 2008) observed its limit behaviour to be equal 1. The striking question concerning this finding was…
John A. P. Sekar, Jose-Juan Tapia, James R. Faeder
Rule-based modeling frameworks provide a specification format in which kinetic interactions are modeled as “reaction rules”. These rules are specified on phosphorylation motifs, domains, binding sites and other sub-molecular structures, and have proved useful for modeling signal transduction. Visual representations are…
Jamshed Khan, Rob Patro
The construction of the compacted de Bruijn graph from a large collection of reference genomes is a task of increasing interest in genomic analyses. For example, compacted colored reference de Bruijn graphs are increasingly used as sequence indices for the purposes of alignment of short and long reads. Also, as we…
Michael Hutcheon, Andrew Teale
Algorithms are presented for performing a topological analysis of an arbitrary function, evaluated on an arbitrary grid of points. These algorithms work strictly by post-processing the data and require no additional function evaluations. This is achieved by connecting the grid points with a neighbourhood graph…
Muhammad Umer Farooq, Muhammad Hussain, Ahmed Zubair Jan, Afraz Hussain Mjaeed + 2 more
In the modern digital sphere, graph theory is a significant field of research that has a great deal of significance. It finds widespread application in computer science, robotic directions, and chemistry. Additionally, graph theory is used in robot network localization, computer network problems and the formation of…
Dorota Kuziak, Ismael G. Yero
The origin of researches concerning metric dimension of graphs is frequently relatively lost in the literature since such concept has arisen in connection with some other related and/or more general areas than that of graphs. For instance, considering the case of metric spaces in general, the notion of metric dimension…
Peter Wills, François G. Meyer
Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience [1], cyber security [2], social network analysis [3], and bioinformatics [4], among others. Discovery and comparison of structures such as modular communities, rich clubs…
Michael Hutcheon, Andrew Teale
Algorithms are presented for performing a topological analysis of an arbitrary function, evaluated on an arbitrary grid of points. These algorithms work strictly by post-processing the data and require no additional function evaluations. This is achieved by connecting the grid points with a neighbourhood graph…
Authors not listed
We present a unified, set–theoretic framework that extends molecular graphs to hypergraphs and superhypergraphs via iterated power sets. We define Molecular Graphs, Molecular HyperGraphs, and Molecular SuperHyperGraphs, and develop four complements over them: Weighted, Rough, Neural, and Multipolar frameworks. We prove…
Benedict Paten, Adam M Novak, Erik Garrison, Glenn Hickey
A superbubble is a type of directed acyclic subgraph with single distinct source and sink vertices. In genome assembly and genetics, the possible paths through a superbubble can be considered to represent the set of possible sequences at a location in a genome. Bidirected and biedged graphs are a generalization of…