thaysa-mo412

At what threshold f c will the network A fall apart if we remove a fraction f of nodes? Will the threshold f c change If we add more 100 levels of a nodes, where all nodes between black nodes and the purple nodes have the same degree as the black nodes (each black node has 4 degree, as depicted in the abstraction of network B)? If so, what is the new value of f c of the network B? f c of A is ~0.729 and f c of B is ~0.749 f c of A is ~0.636 and f c of B is 0.666 f c of A and B are ~0.729 f c of A and B are ~0.636 None of the above Original idea by: Thaysa Bello

Given the network below at t=0, which shows each node and its respective fitness η, the network grows by adding a new node at each subsequent time t. The m is constant and equal to 2, and all new nodes have a fitness of 1. Which node is expected to have the most links at at t=1 and t in the infinity? t=1 is node 1; t=infinity is node 3. t=1 is node 2; t=infinity is node 3. t=1 is node 2; t=infinity is node 5. t=1 is node 3; t=infinity is node 5. None of the above Original idea by: Thaysa Bello

A network starts with 2 nodes and m=1. Use the Barabási–Albert(BA) model to add 8 more nodes to the network, one node at a time for each subsequent t. What is the expected number of links in the network after all nodes have been added? Consider m=1 constant. 8 9 10 16 None of the above Original idea by: Thaysa Bello

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

Regarding random networks, when does the giant component emerge? I: Subcritical \begin{equation*}\langle k \rangle 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...