thaysa-mo412

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

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);

Which of the following adjacency matrices represents a graph that has the same Eulerian path and Hamiltonian path, visiting all nodes and links? \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*} \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*} \begin{equation*} A = \begin{bmatrix} 0 & 1 & 0 & 0 & 0 \\ 1 & 0 & 1 & 0 & 0 \\ 0 & 1 & 0

  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