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Cycles and Starant Graphs for the internet

Authors:
  • IICSE University

Abstract

Counter-examples to the 6-degree theory, starant graphs and cycles, comellas and circulants, and so on.
Cycles and Starant Graphs


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
Six degrees of separation between us and everyone else
on this planet
John Guare, 1990
An urban myth? (“Six handshakes to the President”)
The Very Respected Professor Duncan Watts, from Sociology,
through online material, gave us these quotations. Duncan’s
degrees are called edges in Graph Theory, and our degrees
(from Pure Mathematics) connect to angles or amount of
links originating in a particular vertex.
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
Having access may mean meeting somewhere.
Having a connection must mean being able to contact
the person outside of that somewhere and whenever
intended.
9/':
;
Nobody knows how to contact them, yet they may be
accessible to a few: those who can access them just
don’t know they exist…
Connectivity is zero, accessibility is zero, but potential
accessibility is not zero, and positive.
We are not six degrees away, we are an infinity of
degrees away, for we don’t even know they exist…
9<
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,#  #          
$#    #     ;  $   #
%  $  ## #  #    #"  $
   !   ## #     
##  " #',
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 #      #   # $ # 
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# #' ## 
#)# ###&;<#
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:+  
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  # ?   # .'  $  - 
    # # #   
 # # '  # #  # # 
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'       #  # /
#         #   
A ##'
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9 
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(6
@6!
A6<I9
I
... 1-2) or Milgram's letters (Milgram 1969). The whole interest seems to then be to the side of defining small worlds in a mathematical way (Pinheiro 2018b), and studying step by step the process of 'wiring' between humans from a selected group. ...
Article
Full-text available
In this piece, the paper Deterministic Small-world Communication Networks, a paper from the year of 2000 by Comellas, Ozon, and Peters, is discussed. From the introduction, where some mismatch between sigmatoids, and intended senses is identified, to the conclusion, where the same mismatch appears in the shape of wonder, the findings are of surprising nature: major misunderstandings in the interpretation of the research or teaching or invention of others may lead to great new theories, which may lead to wonderful sets of new, and meaningful mathematical paradigms.
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