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A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set. The result of this application of a weight function is a weighted sum or weighted average .
Sometimes an extension of the domain of the edge weight function to is considered (with the resulting function still being called the edge weight function) by setting (,) = whenever (,). In applications each graph vertex x ∈ V {\displaystyle x\in V} usually represents a single entity in the given data, e.g., elements of a finite data set ...
A directed graph is called weakly connected if replacing all of its directed edges with undirected edges produces a connected (undirected) graph. weight A numerical value, assigned as a label to a vertex or edge of a graph. The weight of a subgraph is the sum of the weights of the vertices or edges within that subgraph. weighted graph
Geometric graph theory in the broader sense is a large and amorphous subfield of graph theory, concerned with graphs defined by geometric means. In a stricter sense, geometric graph theory studies combinatorial and geometric properties of geometric graphs, meaning graphs drawn in the Euclidean plane with possibly intersecting straight-line edges, and topological graphs, where the edges are ...
If s and t are specified vertices of the graph G, then an s – t cut is a cut in which s belongs to the set S and t belongs to the set T. In an unweighted undirected graph, the size or weight of a cut is the number of edges crossing the cut. In a weighted graph, the value or weight is defined by the sum of the weights of the edges crossing the ...
Chemical graph theory uses the molecular graph as a means to model molecules. Graphs and networks are excellent models to study and understand phase transitions and critical phenomena. Removal of nodes or edges leads to a critical transition where the network breaks into small clusters which is studied as a phase transition.
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Intuitively, the graph of a bounded function stays within a horizontal band, while the graph of an unbounded function does not. In mathematics , a function f {\displaystyle f} defined on some set X {\displaystyle X} with real or complex values is called bounded if the set of its values is bounded .