What is...the small-world effect?

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 small world effect? Or: Everyone knows everyone!? 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://www.researchgate.net/profile/Hynek-Lavicka/publication/258120851/figure/fig1/AS:297382332911616@1447912881183/Algorithm-of-Watts-Strogatz-model-which-can-be-tuned-by-parameter-p-0-1.png Small world experiment. https://en.wikipedia.org/wiki/Small-world_experiment https://snap.stanford.edu/class/cs224w-readings/milgram67smallworld.pdf https://snap.stanford.edu/class/cs224w-readings/travers69smallworld.pdf https://en.wikipedia.org/wiki/Six_degrees_of_separation Erdös number and co. https://en.wikipedia.org/wiki/Erd%C5%91s_number https://mathscinet.ams.org/mathscinet/collaborationDistance.html https://en.wikipedia.org/wiki/Six_Degrees_of_Kevin_Bacon#Bacon_numbers Small world network. https://www.nature.com/articles/30918 https://en.wikipedia.org/wiki/Small-world_network http://www.scholarpedia.org/article/Small-world_network https://snap.stanford.edu/class/cs224w-2015/slides/05-smallworlds.pdf https://towardsdatascience.com/what-are-small-world-network-models-87bbcfe0e038 https://mathinsight.org/small_world_network Distance and clustering. https://en.wikipedia.org/wiki/Distance_(graph_theory) https://en.wikipedia.org/wiki/Clustering_coefficient Random graph. https://en.wikipedia.org/wiki/Random_graph https://www.math.cmu.edu/~af1p/BOOK.pdf https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_model#Equivalent_random_network Small-world brain. https://www.sciencedirect.com/science/article/abs/pii/S1364661304001901 https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.320.2809 https://www.cell.com/trends/cognitive-sciences/fulltext/S1364-6613(17)30221-8 https://www.slideshare.net/lshlj82/networks-from-the-small-world-into-the-real-world Mathematica. https://demonstrations.wolfram.com/SmallWorldNetworks/ https://demonstrations.wolfram.com/SamplesOfRandomGraphs/ https://demonstrations.wolfram.com/RandomGraphModels/ Pictures used. https://miro.medium.com/max/1400/0*8T9WFQKlf147X7FE.jpg https://www.johndcook.com/sixdegrees3.png Picture from https://link.springer.com/article/10.1007/s11067-018-9417-y https://media.geeksforgeeks.org/wp-content/uploads/clustering-coefficient-in-graph-theory-1.png Picture from https://snap.stanford.edu/class/cs224w-2015/slides/05-smallworlds.pdf Picture from https://www.sciencedirect.com/science/article/abs/pii/S1364661304001901 Picture from https://www.cell.com/trends/cognitive-sciences/fulltext/S1364-6613(17)30221-8 YouTube and co. https://www.youtube.com/watch?v=A6cCzdUBTjM https://www.youtube.com/watch?v=3QjZ31lj974 https://www.youtube.com/watch?v=XwVZ5VttrW0