WEEK-04 (Optional)


Regarding random networks, when does the giant component emerge?
  1. I: Subcritical \begin{equation*}\langle k \rangle < 1\end{equation*}
  2. II: Critical \begin{equation*}\langle k \rangle = 1\end{equation*}
  3. III: Supercritical \begin{equation*}\langle k \rangle > 1\end{equation*}
  4. IV: Connected \begin{equation*} \langle k \rangle > \ln N\end{equation*}
  5. None of the above
Original idea by: Thaysa Bello

Comentários

Postar um comentário

Postagens mais visitadas deste blog

WEEK-03

Given the following adjacency matrix that represents a directed graph, apply a topological sort using Depth First Search (DFS) and determine the start and finish times for each node. Start from node 'a' and always prioritize visiting nodes in alphabetical order. \begin{equation*} \begin{matrix} & a & b & c & d & e & f & g\\ a & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ b & 0 & 0 & 1 & 0 & 1 & 0 & 0 \\ c & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ d & 0 & 0 & 0 & 0 & 1 & 0 & 1 \\ e & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ f & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ g & 0 & 0 & 0 & 0 & 0 & 1 & 0 \end{matrix} \end{equation*} a(1,14); b(2,13); c(3,12); d(4,11); e(5,10); f(6,7); g(5,8) a(1,14); b(2,13); c(3,12); d(4,11);...
Leia mais

WEEK-01

Imagem
  Five examples are given, each consisting of an adjacency matrix, a graph, and a degree distribution. Example ID Adjacency Matrix Graph Degree Distribution Example I \begin{equation*} A = \begin{bmatrix} 0 & 1 & 0 & 1 & 1 \\ 1 & 0 & 1 & 1 & 0 \\ 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 \end{bmatrix} \end{equation*} Example II \begin{equation*} A = \begin{bmatrix} 0 & 1 & 0 & 0 & 1 \\ 1 & 0 & 1 & 0 & 0 \\ 0 & 1 & 0 & 1 & 0 \\ 0 & 0 & 1 & 0 & 1 \\ 1 & 0 & 0 & 1 & 0 \end{bmatrix} \end{equation*} Example III \begin{equation*} A ...
Leia mais

WEEK-06

Consider a scale-free network with a power-law degree distribution, where the degree exponent is exactly the mean between 2 and 3. The network starts with 1000 nodes, where some nodes have exactly 2 connections and others have more than 2 connections. After some time, the number of nodes grows to be 10 times bigger, and now the minimum degree is 4. By what percentage did k max grow from the initial network to the larger network? k max grows by approximately 100%. k max decreases by approximately 100%. k max grows by approximately 200%. k max decreases by approximately 200%. None of the above Original idea by: Thaysa Bello
Leia mais