What is...the difference between Eulerian and Hamiltonian graphs?

Описание: Goal.
I would like to tell you a bit about my favorite theorems, ideas or concepts in mathematics and why I like them so much.

This time.
What is...the difference between Eulerian and Hamiltonian graphs? Or: They are not dual!?

Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.

Slides.
http://www.dtubbenhauer.com/youtube.html

Thumbnail.
https://en.wikipedia.org/wiki/Hypercu...

Eulerian and Hamiltonian graphs.
https://en.wikipedia.org/wiki/Euleria...
https://en.wikipedia.org/wiki/Hamilto...
https://en.wikipedia.org/wiki/Hamilto...
https://ulsites.ul.ie/cemtl/sites/def...
https://stackoverflow.com/questions/3...
https://math.stackexchange.com/questi...

Line graph and Euler vs. Hamilton.
https://en.wikipedia.org/wiki/Line_graph
https://math.stackexchange.com/questi...

(Non-)Eulerian and (non-)Hamiltonian.
https://math.stackexchange.com/questi...
http://oeis.org/A003049
http://oeis.org/A003216
https://mathworld.wolfram.com/Noneule...
http://oeis.org/A158007
https://mathworld.wolfram.com/Nonhami...
http://oeis.org/A246446

Number of connected graphs.
http://oeis.org/A001349

Bondy-Chvátal and co.
https://en.wikipedia.org/wiki/Hamilto...
https://en.wikipedia.org/wiki/Ore%27s...
https://www.theoremoftheday.org/Combi...
https://proofwiki.org/wiki/Ore%27s_Th...

Bridges in Königsberg.
https://en.wikipedia.org/wiki/Seven_B...
https://www.maa.org/press/periodicals...
https://mathworld.wolfram.com/Koenigs...
https://math.stackexchange.com/questi...

Mathematica.
https://reference.wolfram.com/languag...
https://reference.wolfram.com/languag...
https://reference.wolfram.com/languag...
https://reference.wolfram.com/languag...
https://demonstrations.wolfram.com/Th...

Pictures used.
https://en.wikipedia.org/wiki/Seven_B...
https://en.wikipedia.org/wiki/Seven_B...

The bridges of Königsberg and friends are very popular.
   • Hamiltonian and semi hamiltonian graphs  
   • How the Königsberg bridge problem changed ...  
   • The Seven Bridges of Königsberg - Numberphile  
   • Konigsberg Bridge Problem  
   • Ore’s Theorem