“Two-scale” network?












0












$begingroup$


I've read that networks can be:




  • random (Erdős–Rényi model),


  • scale-free (Albert–Barabási model),


  • small-world (Watts–Strogatz model).



But can a real world network be “two-scale”, in the sense that its degree distribution only consists of two different degrees, for example $(5,5,5,5,4,4,4,...)$ where the number nodes of degree $4$ is equal to $9$?










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$endgroup$












  • $begingroup$
    Real world, no. But for a random network as you wish, yes, simply adapt the usual construction starting with half-edges attached to each vertex.
    $endgroup$
    – Did
    Aug 28 '18 at 5:57










  • $begingroup$
    It can't be real world because it doesn't have a power law degree distribution? Would the degree distribution for a "two scale" network just be a line segment with negative slope?
    $endgroup$
    – Ultradark
    Aug 28 '18 at 13:17










  • $begingroup$
    It can't be real world because it doesn't have a power law degree distribution? – Many real networks do not have such a distribution and it is still up to debate to what extents observations of such distributions in real networks are a measurement artefact. The models you list are just that: models. Any given real network will substantially differ from the typical output of these models. (And note that I use typical here only because all of the models involve randomness and therefore can produce all sorts of things with a very low probability.)
    $endgroup$
    – Wrzlprmft
    Jan 14 at 18:25


















0












$begingroup$


I've read that networks can be:




  • random (Erdős–Rényi model),


  • scale-free (Albert–Barabási model),


  • small-world (Watts–Strogatz model).



But can a real world network be “two-scale”, in the sense that its degree distribution only consists of two different degrees, for example $(5,5,5,5,4,4,4,...)$ where the number nodes of degree $4$ is equal to $9$?










share|cite|improve this question











$endgroup$












  • $begingroup$
    Real world, no. But for a random network as you wish, yes, simply adapt the usual construction starting with half-edges attached to each vertex.
    $endgroup$
    – Did
    Aug 28 '18 at 5:57










  • $begingroup$
    It can't be real world because it doesn't have a power law degree distribution? Would the degree distribution for a "two scale" network just be a line segment with negative slope?
    $endgroup$
    – Ultradark
    Aug 28 '18 at 13:17










  • $begingroup$
    It can't be real world because it doesn't have a power law degree distribution? – Many real networks do not have such a distribution and it is still up to debate to what extents observations of such distributions in real networks are a measurement artefact. The models you list are just that: models. Any given real network will substantially differ from the typical output of these models. (And note that I use typical here only because all of the models involve randomness and therefore can produce all sorts of things with a very low probability.)
    $endgroup$
    – Wrzlprmft
    Jan 14 at 18:25
















0












0








0





$begingroup$


I've read that networks can be:




  • random (Erdős–Rényi model),


  • scale-free (Albert–Barabási model),


  • small-world (Watts–Strogatz model).



But can a real world network be “two-scale”, in the sense that its degree distribution only consists of two different degrees, for example $(5,5,5,5,4,4,4,...)$ where the number nodes of degree $4$ is equal to $9$?










share|cite|improve this question











$endgroup$




I've read that networks can be:




  • random (Erdős–Rényi model),


  • scale-free (Albert–Barabási model),


  • small-world (Watts–Strogatz model).



But can a real world network be “two-scale”, in the sense that its degree distribution only consists of two different degrees, for example $(5,5,5,5,4,4,4,...)$ where the number nodes of degree $4$ is equal to $9$?







soft-question network






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share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jan 14 at 18:20









Wrzlprmft

3,17111335




3,17111335










asked Aug 28 '18 at 2:54









UltradarkUltradark

3631518




3631518












  • $begingroup$
    Real world, no. But for a random network as you wish, yes, simply adapt the usual construction starting with half-edges attached to each vertex.
    $endgroup$
    – Did
    Aug 28 '18 at 5:57










  • $begingroup$
    It can't be real world because it doesn't have a power law degree distribution? Would the degree distribution for a "two scale" network just be a line segment with negative slope?
    $endgroup$
    – Ultradark
    Aug 28 '18 at 13:17










  • $begingroup$
    It can't be real world because it doesn't have a power law degree distribution? – Many real networks do not have such a distribution and it is still up to debate to what extents observations of such distributions in real networks are a measurement artefact. The models you list are just that: models. Any given real network will substantially differ from the typical output of these models. (And note that I use typical here only because all of the models involve randomness and therefore can produce all sorts of things with a very low probability.)
    $endgroup$
    – Wrzlprmft
    Jan 14 at 18:25




















  • $begingroup$
    Real world, no. But for a random network as you wish, yes, simply adapt the usual construction starting with half-edges attached to each vertex.
    $endgroup$
    – Did
    Aug 28 '18 at 5:57










  • $begingroup$
    It can't be real world because it doesn't have a power law degree distribution? Would the degree distribution for a "two scale" network just be a line segment with negative slope?
    $endgroup$
    – Ultradark
    Aug 28 '18 at 13:17










  • $begingroup$
    It can't be real world because it doesn't have a power law degree distribution? – Many real networks do not have such a distribution and it is still up to debate to what extents observations of such distributions in real networks are a measurement artefact. The models you list are just that: models. Any given real network will substantially differ from the typical output of these models. (And note that I use typical here only because all of the models involve randomness and therefore can produce all sorts of things with a very low probability.)
    $endgroup$
    – Wrzlprmft
    Jan 14 at 18:25


















$begingroup$
Real world, no. But for a random network as you wish, yes, simply adapt the usual construction starting with half-edges attached to each vertex.
$endgroup$
– Did
Aug 28 '18 at 5:57




$begingroup$
Real world, no. But for a random network as you wish, yes, simply adapt the usual construction starting with half-edges attached to each vertex.
$endgroup$
– Did
Aug 28 '18 at 5:57












$begingroup$
It can't be real world because it doesn't have a power law degree distribution? Would the degree distribution for a "two scale" network just be a line segment with negative slope?
$endgroup$
– Ultradark
Aug 28 '18 at 13:17




$begingroup$
It can't be real world because it doesn't have a power law degree distribution? Would the degree distribution for a "two scale" network just be a line segment with negative slope?
$endgroup$
– Ultradark
Aug 28 '18 at 13:17












$begingroup$
It can't be real world because it doesn't have a power law degree distribution? – Many real networks do not have such a distribution and it is still up to debate to what extents observations of such distributions in real networks are a measurement artefact. The models you list are just that: models. Any given real network will substantially differ from the typical output of these models. (And note that I use typical here only because all of the models involve randomness and therefore can produce all sorts of things with a very low probability.)
$endgroup$
– Wrzlprmft
Jan 14 at 18:25






$begingroup$
It can't be real world because it doesn't have a power law degree distribution? – Many real networks do not have such a distribution and it is still up to debate to what extents observations of such distributions in real networks are a measurement artefact. The models you list are just that: models. Any given real network will substantially differ from the typical output of these models. (And note that I use typical here only because all of the models involve randomness and therefore can produce all sorts of things with a very low probability.)
$endgroup$
– Wrzlprmft
Jan 14 at 18:25












1 Answer
1






active

oldest

votes


















1












$begingroup$

The concept of “real-world networks” is not well defined. Usually, as soon as you find some kind of natural data, from which your network emerges it can be considered a real-world network. Most real-world data has certain properties that are significantly different from random networks (i.e., the Erdős–Rényi model), e.g., its degree distribution or the small-world property.



If you are asking whether there exists a graph that has that particular degree sequence, then the answer is yes, and here is an example given by its edge list:
$
[(0, 11), ;
(0, 3), ;
(0, 3), ;
(0, 10), ;
(0, 6), ;
(1, 4), ;
(1, 3), ;
(1, 11), ;
(1, 10), ;
(1, 5), ;
(2, 5), ;
(2, 7), ;
(2, 7), ;
(2, 4), ;
(2, 3), ;
(3, 5), ;
(4, 8), ;
(4, 8), ;
(5, 6), ;
(6, 9), ;
(6, 11), ;
(7, 7), ;
(8, 12), ;
(8, 10), ;
(9, 10), ;
(9, 12), ;
(9, 11), ;
(12, 12)]$



In general, this is known as the graph-realization problem and there are efficient (i.e. in polynomial time) algorithms that, given a degree sequence, can decide whether this sequence can be realized as a degree sequence of a graph or not.



Also note that networks can fall in much more than just these three categories, and the Watts–Strogatz model with $0$ randomness actually does not exhibit the small-world property.






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    1 Answer
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    active

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    active

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    1












    $begingroup$

    The concept of “real-world networks” is not well defined. Usually, as soon as you find some kind of natural data, from which your network emerges it can be considered a real-world network. Most real-world data has certain properties that are significantly different from random networks (i.e., the Erdős–Rényi model), e.g., its degree distribution or the small-world property.



    If you are asking whether there exists a graph that has that particular degree sequence, then the answer is yes, and here is an example given by its edge list:
    $
    [(0, 11), ;
    (0, 3), ;
    (0, 3), ;
    (0, 10), ;
    (0, 6), ;
    (1, 4), ;
    (1, 3), ;
    (1, 11), ;
    (1, 10), ;
    (1, 5), ;
    (2, 5), ;
    (2, 7), ;
    (2, 7), ;
    (2, 4), ;
    (2, 3), ;
    (3, 5), ;
    (4, 8), ;
    (4, 8), ;
    (5, 6), ;
    (6, 9), ;
    (6, 11), ;
    (7, 7), ;
    (8, 12), ;
    (8, 10), ;
    (9, 10), ;
    (9, 12), ;
    (9, 11), ;
    (12, 12)]$



    In general, this is known as the graph-realization problem and there are efficient (i.e. in polynomial time) algorithms that, given a degree sequence, can decide whether this sequence can be realized as a degree sequence of a graph or not.



    Also note that networks can fall in much more than just these three categories, and the Watts–Strogatz model with $0$ randomness actually does not exhibit the small-world property.






    share|cite|improve this answer











    $endgroup$


















      1












      $begingroup$

      The concept of “real-world networks” is not well defined. Usually, as soon as you find some kind of natural data, from which your network emerges it can be considered a real-world network. Most real-world data has certain properties that are significantly different from random networks (i.e., the Erdős–Rényi model), e.g., its degree distribution or the small-world property.



      If you are asking whether there exists a graph that has that particular degree sequence, then the answer is yes, and here is an example given by its edge list:
      $
      [(0, 11), ;
      (0, 3), ;
      (0, 3), ;
      (0, 10), ;
      (0, 6), ;
      (1, 4), ;
      (1, 3), ;
      (1, 11), ;
      (1, 10), ;
      (1, 5), ;
      (2, 5), ;
      (2, 7), ;
      (2, 7), ;
      (2, 4), ;
      (2, 3), ;
      (3, 5), ;
      (4, 8), ;
      (4, 8), ;
      (5, 6), ;
      (6, 9), ;
      (6, 11), ;
      (7, 7), ;
      (8, 12), ;
      (8, 10), ;
      (9, 10), ;
      (9, 12), ;
      (9, 11), ;
      (12, 12)]$



      In general, this is known as the graph-realization problem and there are efficient (i.e. in polynomial time) algorithms that, given a degree sequence, can decide whether this sequence can be realized as a degree sequence of a graph or not.



      Also note that networks can fall in much more than just these three categories, and the Watts–Strogatz model with $0$ randomness actually does not exhibit the small-world property.






      share|cite|improve this answer











      $endgroup$
















        1












        1








        1





        $begingroup$

        The concept of “real-world networks” is not well defined. Usually, as soon as you find some kind of natural data, from which your network emerges it can be considered a real-world network. Most real-world data has certain properties that are significantly different from random networks (i.e., the Erdős–Rényi model), e.g., its degree distribution or the small-world property.



        If you are asking whether there exists a graph that has that particular degree sequence, then the answer is yes, and here is an example given by its edge list:
        $
        [(0, 11), ;
        (0, 3), ;
        (0, 3), ;
        (0, 10), ;
        (0, 6), ;
        (1, 4), ;
        (1, 3), ;
        (1, 11), ;
        (1, 10), ;
        (1, 5), ;
        (2, 5), ;
        (2, 7), ;
        (2, 7), ;
        (2, 4), ;
        (2, 3), ;
        (3, 5), ;
        (4, 8), ;
        (4, 8), ;
        (5, 6), ;
        (6, 9), ;
        (6, 11), ;
        (7, 7), ;
        (8, 12), ;
        (8, 10), ;
        (9, 10), ;
        (9, 12), ;
        (9, 11), ;
        (12, 12)]$



        In general, this is known as the graph-realization problem and there are efficient (i.e. in polynomial time) algorithms that, given a degree sequence, can decide whether this sequence can be realized as a degree sequence of a graph or not.



        Also note that networks can fall in much more than just these three categories, and the Watts–Strogatz model with $0$ randomness actually does not exhibit the small-world property.






        share|cite|improve this answer











        $endgroup$



        The concept of “real-world networks” is not well defined. Usually, as soon as you find some kind of natural data, from which your network emerges it can be considered a real-world network. Most real-world data has certain properties that are significantly different from random networks (i.e., the Erdős–Rényi model), e.g., its degree distribution or the small-world property.



        If you are asking whether there exists a graph that has that particular degree sequence, then the answer is yes, and here is an example given by its edge list:
        $
        [(0, 11), ;
        (0, 3), ;
        (0, 3), ;
        (0, 10), ;
        (0, 6), ;
        (1, 4), ;
        (1, 3), ;
        (1, 11), ;
        (1, 10), ;
        (1, 5), ;
        (2, 5), ;
        (2, 7), ;
        (2, 7), ;
        (2, 4), ;
        (2, 3), ;
        (3, 5), ;
        (4, 8), ;
        (4, 8), ;
        (5, 6), ;
        (6, 9), ;
        (6, 11), ;
        (7, 7), ;
        (8, 12), ;
        (8, 10), ;
        (9, 10), ;
        (9, 12), ;
        (9, 11), ;
        (12, 12)]$



        In general, this is known as the graph-realization problem and there are efficient (i.e. in polynomial time) algorithms that, given a degree sequence, can decide whether this sequence can be realized as a degree sequence of a graph or not.



        Also note that networks can fall in much more than just these three categories, and the Watts–Strogatz model with $0$ randomness actually does not exhibit the small-world property.







        share|cite|improve this answer














        share|cite|improve this answer



        share|cite|improve this answer








        edited Jan 14 at 18:18









        Wrzlprmft

        3,17111335




        3,17111335










        answered Jan 14 at 17:52









        chickenNinja123chickenNinja123

        14313




        14313






























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