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A regular graph is one in which each vertex has the same number of neighbors, but in a star topology the central vertex is connected to more than one vertex. So, why is it referred to as a regular graph?

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Star topology is not a regular graph. – Pratik Deoghare Jan 3 '13 at 1:38
In this research paper "Quantitative Comparison of Graph-Based Models for Internet Topology", they have considered it to be a regular graph – Xara Jan 3 '13 at 1:43
Of the four examples in Fig 3 of "Quantitative...", only the ring is a regular graph. This leads me the believe that they don't mean regular in the way you think, but instead simply mean a graph with nice/predictable structure. – Marc Khoury Jan 3 '13 at 1:56
Then that paper is also wrong unless authors mean something else by regular. Regular is one of the most overloaded words in math. – Pratik Deoghare Jan 3 '13 at 2:14

summarizing the comments: by the standard definition, a star is not a regular graph.

They might defined "regular" in a different way than common to apply to star topology. Specifically, in the paper the OP point out "regular" is never defined (and sparsely used).

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