Degree Correlations

In a digital activism campaign, hashtags often appear together in posts about different causes. Each hashtag is a node, and an edge between two hashtags means they frequently co-occur. Some hashtags become hubs of influence, connecting many others and shaping which causes gain more visibility. Even algorithms designed to be neutral may reinforce certain hierarchies — after all, Politics is Never Neutral.

Consider the imagem below and the following hashtag co-occurrence network:

  • #InnovationForGood (Node 1): k = 4
  • #SocialJustice (Node 2): k = 3
  • #ClimateAction (Node 3): k = 3
  • #HealthForAll (Node 4): k = 2
  • #EducationMatters (Node 5): k = 1
  • #GenderRights (Node 6): k = 1
  • Compute the average nearest neighbor degree knn for #InnovationForGood (Node 1).
  • Compute the degree assortativity coefficient for the entire network (using the Pearson correlation of degrees).
  • Interpret whether this network shows assortative or disassortative mixing, and the impact.

Which of the following statements is correct?

  1. knn = 2.25; r = +0.56; the network is assortative and promotes equality.
  2. knn = 2.25; r = -0.46; the network is disassortative, showing unequal visibility.
  3. knn = 3.25; r = -0.56; the network is disassortative but neutral in visibility.
  4. knn = 3.25; r = +0.46; the network is assortative, showing unequal visibility.
  5. None of the above

Original idea by: Aline Azevedo

Comments

Post a Comment

Popular posts from this blog

Dogs, Friends, and Paths at Praça da Paz

Image
Six dogs are happily playing at Praça da Paz, Barão Geraldo . Each dog is a node , and each friendship (two dogs playing together) is an edge .   Considering the above  undirected network of dog friendships, which of the following statements is correct ? A)  The clustering coefficient of node Violeta is 0 B)  Ginger is very social and her clustering coefficient is 0.5, participating in more than one triangle C) The shortest path from Mindú to Violeta has length 4 D)  The average degree of the nodes ⟨k⟩  is 2.375, and the degree distribution shows that three nodes have degree 1 E)   None of the above   Original idea by: Aline Azevedo
Read more

Barabási–Albert Model

You are an analyst for a streaming platform called StreamWorld , which works like a social network: each movie is a node, and connections between movies represent users who watched both. StreamWorld grows following a pattern similar to the Barabási–Albert model : Each new movie connects to m = 3 existing movies. The probability of a movie receiving a new connection is proportional to the number of connections it already has (preferential attachment). At the start ( t = 0 ), there are m₀ = 5 fully connected movies. At time t = 12000 , the network has N = 12000 + m₀ movies, and three movies were released: - Movie A at t A = 100 - Movie B at t B = 1000 - Movie C at t C = 4000 Which of the following is the correct ranking of their expected degrees k i (t) from largest to smallest , what is the approximate ratio between the larges...
Read more

Random Graph - Erdős-Rényi

Consider a connected Erdős-Rényi random graph \( G(n, p) \) with \( n = 100 \) nodes and edge probability \( p = 0.1 \). The average degree is \( \langle k \rangle = 10 \). Which of the following statements is correct? The degree distribution is concentrated around the mean, the average distance scales linearly with \( n \), and the clustering coefficient is \( 0.05 \). The degree distribution is approximately Poisson, the average distance is 2, and the clustering coefficient is roughly equal to \( p \). The degree distribution is uniform, the average distance is independent of \( n \), and the clustering coefficient grows with \( n \). The degree distribution is Poisson, the average distance is 3, and the clustering coefficient is zero. None of the above Original idea by: Aline Azevedo
Read more