scholarly journals A weighted graph polynomial from chromatic invariants of knots

1999 ◽  
Vol 49 (3) ◽  
pp. 1057-1087 ◽  
Author(s):  
Steven D. Noble ◽  
Dominic J. A. Welsh
Keyword(s):  
Weighted Graph ◽  
Graph Polynomial

scholarly journals Evaluating a Weighted Graph Polynomial for Graphs of Bounded Tree-Width

10.37236/153 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
S. D. Noble
Keyword(s):  
Polynomial Time ◽  
Weighted Graph ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Graph Polynomial ◽  
Tree Width

We show that for any $k$ there is a polynomial time algorithm to evaluate the weighted graph polynomial $U$ of any graph with tree-width at most $k$ at any point. For a graph with $n$ vertices, the algorithm requires $O(a_k n^{2k+3})$ arithmetical operations, where $a_k$ depends only on $k$.

Approach to spatial modeling of networks and groups of objects on the basis of the weighted graph construction procedure

2020 ◽  
Vol 964 (10) ◽  
pp. 49-58
Author(s):  
V.I. Bilan ◽  
A.N. Grigor’ev ◽  
G.G. Dmitrikov ◽  
E.A. Dudin
Keyword(s):  
Spatial Configuration ◽  
Weighted Graph ◽  
Edge Length ◽  
Buffer Zones ◽  
Typical Structure ◽  
Spatial Graph ◽  
Object Based ◽  
Complementary Graph ◽  
Spatial Parameters ◽  
The Given

The direction of research on the development of a scientific and methodological tool for the analysis of spatial objects in order to determine their generalized spatial parameters was selected. An approach to the problem of modeling networks and groups of objects based on the synthesis of a weighted graph is proposed. The spatial configuration of objects based on the given conditions is described by a weighted graph, the edge length of which is considered as the weight of the edges. A generalization to the typical structure of a spatial graph is formulated; its essence is representation of nodal elements as two-dimensional (polygonal) objects. To take into account the restrictions on the convergence of the vertices described by the buffer zones, a complementary graph is formed. An algorithm for constructing the implementation of a spatial object based on the sequential determination of vertices that comply with the given conditions is proposed. Using the software implementation of the developed algorithm, an experiment was performed to evaluate the spatial parameters of the simulated objects described by typical graph structures. The following parameters were investigated as spatial ones

Kernelized multi-view subspace clustering via auto-weighted graph learning

2021 ◽  
Author(s):  
Guang-Yu Zhang ◽  
Xiao-Wei Chen ◽  
Yu-Ren Zhou ◽  
Chang-Dong Wang ◽  
Dong Huang ◽  
...  
Keyword(s):  
Subspace Clustering ◽  
Weighted Graph ◽  
Graph Learning

Nodes-weighted-graph approach for rsfMRI data classification: Application to schizophrenia

2016 ◽  
Author(s):  
Xue Mei ◽  
Weiwei Li ◽  
Ryad Chellali ◽  
Yu Zhou ◽  
Jiashuang Huang ◽  
...  
Keyword(s):  
Weighted Graph ◽  
Data Classification

scholarly journals Spread of Epidemic Disease on Edge-Weighted Graphs from a Database: A Case Study of COVID-19

2021 ◽  
Vol 18 (9) ◽  
pp. 4432
Author(s):  
Ronald Manríquez ◽  
Camilo Guerrero-Nancuante ◽  
Felipe Martínez ◽  
Carla Taramasco
Keyword(s):  
Public Health ◽  
Infectious Diseases ◽  
Preventive Measures ◽  
Weighted Graph ◽  
Real Data ◽  
Sir Model ◽  
Weighted Graphs ◽  
Epidemic Disease ◽  
The Real

The understanding of infectious diseases is a priority in the field of public health. This has generated the inclusion of several disciplines and tools that allow for analyzing the dissemination of infectious diseases. The aim of this manuscript is to model the spreading of a disease in a population that is registered in a database. From this database, we obtain an edge-weighted graph. The spreading was modeled with the classic SIR model. The model proposed with edge-weighted graph allows for identifying the most important variables in the dissemination of epidemics. Moreover, a deterministic approximation is provided. With database COVID-19 from a city in Chile, we analyzed our model with relationship variables between people. We obtained a graph with 3866 vertices and 6,841,470 edges. We fitted the curve of the real data and we have done some simulations on the obtained graph. Our model is adjusted to the spread of the disease. The model proposed with edge-weighted graph allows for identifying the most important variables in the dissemination of epidemics, in this case with real data of COVID-19. This valuable information allows us to also include/understand the networks of dissemination of epidemics diseases as well as the implementation of preventive measures of public health. These findings are important in COVID-19’s pandemic context.

scholarly journals Free Product C* -algebras Associated with Graphs, Free Differentials, and Laws of Loops

2017 ◽  
Vol 69 (3) ◽  
pp. 548-578 ◽  
Author(s):  
Michael Hartglass
Keyword(s):  
Differential Calculus ◽  
Von Neumann Algebras ◽  
Sufficient Conditions ◽  
Weighted Graph ◽  
Positive Cone ◽  
Von Neumann ◽  
Planar Algebras ◽  
C Algebra ◽  
C Algebras ◽  
Necessary And Sufficient

AbstractWe study a canonical C* -algebra, 𝒮(Г,μ), that arises from a weighted graph (Г,μ), speci fic cases of which were previously studied in the context of planar algebras. We discuss necessary and sufficient conditions of the weighting that ensure simplicity and uniqueness of trace of 𝒮(Г,μ), and study the structure of its positive cone. We then study the *-algebra,𝒜, generated by the generators of 𝒮(Г,μ), and use a free differential calculus and techniques of Charlesworth and Shlyakhtenko as well as Mai, Speicher, and Weber to show that certain “loop” elements have no atoms in their spectral measure. After modifying techniques of Shlyakhtenko and Skoufranis to show that self adjoint elements x ∊ Mn(𝒜) have algebraic Cauchy transform, we explore some applications to eigenvalues of polynomials inWishart matrices and to diagrammatic elements in von Neumann algebras initially considered by Guionnet, Jones, and Shlyakhtenko.

Efficient Initial Pool Generation for Weighted Graph Problems Using Parallel Overlap Assembly

2005 ◽  
pp. 215-223 ◽  
Author(s):  
Ji Youn Lee ◽  
Hee-Woong Lim ◽  
Suk-In Yoo ◽  
Byoung-Tak Zhang ◽  
Tai Hyun Park
Keyword(s):  
Weighted Graph ◽  
Graph Problems
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