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About 1,375 papers for “Multigraph”

Molecular MultiGraph and Molecular Iterative MultiGraph

Toshio Fujita · ChemRxiv · 2025

A multigraph permits multiple edges between the same pair of vertices, allowing the modeling of repeated or parallel relationships in networks and systems. An iterative multigraph is obtained by repeatedly applying multigraph transformations, generating a sequence of graphs that capture evolving multi-edge connectivity patterns. A molecular graph represents the structure of a chemical compound, where vertices correspond to atoms and edges represent chemical bonds. A molecular multigraph extends this concept by allowing multiple bonds (edges) between the same pair of atoms (vertices). Since research on iterative multigraphs is still in its early stages, applications in chemistry and related domains remain largely unexplored. In this paper, we present the formal definition of the Molecular Iterative-MultiGraph.

Cited by 0Open access

Multigraph PETs

Richard Schwartz · Mathematical surveys and monographs · 2014

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Multigraph Modeling

Harry J. Khamis · Wiley StatsRef: Statistics Reference Online · 2014

Abstract Multigraph modeling makes use of mathematical graph theory to analyze and interpret hierarchical loglinear models. For a given such model, a multigraph is constructed, and from the multigraph, decomposability is determined from a simple combinatorial identity; factorization of the joint distribution is based on a maximum spanning tree; and the conditional independence interpretation comes from the edge cutsets.

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Multigraph of multigraphs

Zbigniew Oziewicz, Fernando R. Velázquez–Quesada · UvA-DARE (University of Amsterdam) · 2009

An n-category is a n-graph (a multigraph) with an algebraic structure. We introduce a graph of graphs and, for a k-tuple of natural numbers n(i) ∈ N, an (n(1),...,n(k))-graph: a (n(1),...,n(i))-graph of (n(i+1),...,n(k))-graphs for 1 ≤ i < k. A multigraph of multigraphs include, among others, the concepts of a prefunctor and a prenatural transformation as more fundamental concepts than functor and natural transformation. The presented formalism gives the appropriate mathematical foundations for multi-scale analysis of hierarchical systems, among other applications. Several examples are considered.

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The Multigraph Modeling Tool

C. A. Childers, A. W. Apon, W. H. Hooper et al. · 2007

The Multigraph Modeling Tool (MMT) has been developed as a performance prediction tool for parallel applications executing on multicomputer systems. MMT is a program generator that accepts as input a system description (i.e., a parallel application and the hardware on which it executes) and from this description automatically generates an analytic model which can be used to predict the performance of the system. The solution of the analytic model results in standard performance metrics such as processor utilization and application response time. A change in a parameter of the system description results in MMT automatically generating a new analytic model. The different sets of metrics produced for a system by varying description parameters can be used by engineers to determine those parameters which result in the best performance. MMT has been applied to a network of RS6000 workstations and to an Intel Paragon. 1. Introduction With the wide availability of high--powered computing res...

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ON MULTIGRAPH EXTREMAL PROBLEMS

W G. Brown, P. Erdős, M Simonovits · 2012

Nous considérons des multigraphes (resp. graphes orientés) ayant au plus r arétes entre deux sommets (resp. r arcs reliant un sommet á un autre). Dans cet article nous donnons des résultats connus et nouveaux concernant le probléme suivant: étant donné une famille de multigraphes (resp. graphes orientés) A 1,..., A k du type ci-dessus, quel est le nombre maximum d'arétes (resp. arcs) que peut avoir un multigraphe (resp. graphe orienté) du type ci-dessus ne contenant aucun A; comme sous-multigraphe (sous-graphe) partiel.

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Purchase Order: Addressograph-Multigraph

Purchasing Division, State of Kansas Department of Administration · FHSU Scholars Repository (Fort Hays State University) · 1967

This black and white one page document features a purchase order for library equipment from Addressograph-Multigraph of Wichita, Kansas.

Cited by 0Open access