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WEEK14 - Network flow

Consider a flow network for the company "A", which needs to deliver products from the capital to 10 cities. Three of these cities are small and don't have direct delivery routes from the capital. However, each of these small cities can receive products from the other 7 cities. Due to a special event, City "T", one of the three small cities, requires a delivery of 650 products. The flow capacities of the network are defined as follows: Company "A" can send a maximum of 150 products to each city that has a direct connection from the capital Two of the 7 cities that can receive products directly from the capital can forward a maximum of 200 products each to City "T". The remaining 5 of the 7 cities can forward a maximum of 50 products each to City "T". The other two small cities don't require any products. Given these conditions, how many of the 650 requested products can be delivered to City "T" for
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WEEK-12 - Network Robustness

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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
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WEEK-10 - Evolving Networks

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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
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WEEK-08 - Barabási–Albert (BA)

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
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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
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WEEK-04 (Optional)

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
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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);
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