A weighted graph is a graph in which each edge is assigned a numerical value, known as the weight. The weight represents the cost, distance, or any other metric that quantifies the relationship between two vertices. Weighted graphs are extensively used in applications such as network routing,...
Weighted graphs in graph theory are created by weighing different values depending on the importance of connections or centers in a graph model. Networks can be modeled with graphs such that the devices and centers correspond to the vertices and connections correspond to the edges. In these ...
Graph theory Weighted graph A weighted graph has a number assigned to each of its edges, called its weight. The weight can be used to represent distances or capacities. A weighted graph is shown in Figure 19.5. Sign in to download full-size image Figure 19.5. A weighted graph. View chapte...
1)weighted graph加权图 1.A new spatio-temporal data model based on graph theory is presented,the organizing strategy of spatio-temporal data based on weighted graph is studied,and a formalized method to describe spatio-temporal semanteme is provided.以计算机通用的数据结构———图为基础,研究了基于...
spectral characterisation of bipartite graphs with unweighted vertices (which are here termed homogeneous graphs) is extended to those bipartite graphs (called heterogeneous) in which all of the vertices in one set are weighted h 1 , and each of those in the other set of the bigraph is weighte...
We give an especially simple proof of a theorem in graph theory that forms the key part of the solution to a problem in commutative algebra, on how to characterize the integral closure of a polynomial ring generated by quadratic monomials....
Using the language of graph theory two methods of partitioning V are examined. In one method, partitionings of V are obtained by selecting threshold values and applying them to a maximal weighted spanning forest. In another method a parametric linear program is used to obtain a “most adhesive...
The network comparison comes from the graph comparison in graph theory. Early graph comparison methods, such as graph isomorphism21,22 and edit distance23,24,25, are mainly based on graph matching26 technology to decide whether two graphs are identical. Generally, the algorithms have the time com...
We also show that a pseudofactorization for such a graph can be computed in O(mn) time, plus the time to solve APSP, resulting in an O(mn+n2loglogn) running time. Introduction The task of finding isometric embeddings, or mappings of the vertex set of one graph to another while ...
In spectral graph theory, matrices associated with a graph G play an important role. Thus, using a matrix to represent the structure of a molecular graph with edge-weights separately on its pairs of adjacent vertices, it would be much better keep the structural information of the graph. In ...