graphs and euclidean space

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So, was reading an online blog and it said most real world data comes in the form of graphs and do not lie in a Euclidean space.

I am not able to fully appreciate this comment. What are the properties of the Euclidean space which cannot be present in a graph representation?

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Distances are not preserved. The distance between two vertices in a graph is defined by the length of a shortest path connected them. But if you try to embed a graph $G$ into a Euclidean metric space, which is equipped with the Euclidean distance metric, it can shorten the distance between those points. The difference between distances in $G$ and in the metric space it embeds into is called the distortion. There are more details in these lecture notes: http://web.stanford.edu/class/cs369m/cs369mlecture1.pdf