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What Is a Graph? Three Possible Answers

What is a graph? What is it that makes one graph different (nonisomorphic) from another? What is the essence of this object we call a graph? We will investigate three viewpoints on these questions, only the last of which seems to hold out any promise of leading to fruitful results. This paper is more of an expository one than one containing new research. It will certainly present more questions than answers. It will also point to some possible directions for future work. The three viewpoints are: A graph is the result of an evolutionary process, Capobianco and Frank [4]; a graph is a n equivalence class of strings of integers, Patterson [6]; a graph is a collection of distributions, Buckley [ l ] , also Quintas et al.