# Fuzzy Graphs

• John N. Mordeson
• Premchand S. Nair
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 20)

## Abstract

Any relation R ⊒ S × S on a set can be regarded as defining a graph with vertex set S and edge set R. That is, a graph is a pair (S, R), where S is a set and R is a relation on S. Similarly, any fuzzy relation R on a fuzzy subset Ã of a set S can be regarded as defining a weighted graph, or fuzzy graph, where the edge (x,y) ∈ S × S has weight or strength R(x,y)∈[0,1].

## Keywords

Fuzzy Subset Fuzzy Relation Connected Subgraph Fuzzy Graph Weak Edge
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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