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Matching networks, matrices, and dendrograms

Consider the three small networks below, the adjacency matrix M, and the three dendrograms in shuffled order produced by hierarchical clustering applied to each graph's shortest-path distance matrix, where the dashed red line shows a cut that creates community partitions. Graph A 1 2 3 4 5 6 Graph B 1 2 3 4 5 6 Graph C 1 2 3 4 5 6 Dendrogram 1 1 2 3 4 5 6 Dendrogram 2 1 2 3 4 5 6 Dendrogram 3 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 0 1 1 0 0 0 1 0 1 0 0 0 1 1 0 1 0 0 0 0 ...
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Pearson degree-correlation coefficient

Consider the network below: A B C D E What is the Pearson degree correlation coefficient (r) for this network using Mark Newman's definition? A. r = 0, since the average degree of every node’s neighbors equals ⟨k⟩. B. r = -2/3, indicating the network is assortative. C. r = +2/3, indicating the network is disassortative. D. r = -1/2, indicating the network is assortative. E. None of the above. Original idea by: Gustavo P. C. P. da Luz
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Ratio of k in Barabasi-Albert model

In a Barabási-Albert model with m = 2, node A is added at time tA= 1 and node B at time tB = 4, as illustrated in the Figure. Here tA and tB are the birth times t i of each node. What is the ratio kA(100) / kB(100)? t k 0 5 10 15 20 1 4 25 50 100 node B enters (tB=4) node A (tA=1) kA(100) kB(100) 1/2 1 4 10 None of the above Original idea by: Gustavo P. C. P. da Luz
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Quiz - Scale-free networks

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The figure below shows the Complementary Cumulative Distribution Function (CCDF) $P(K > k)$ on a log-log scale for two networks, both with $N = 10^4$ nodes and $k_{\min} = 1$. Network A has $\gamma = 2.1$ and network B has $\gamma = 2.9$.   In what range does the ratio ($r$) of the largest hub in network A to the largest hub in network B fall? $0 \leq r \lt 10$ $10 \leq r \lt 20$ $20 \leq r \lt 30$ $30 \leq r \lt 40$ None of the above Original idea by: Gustavo P. C. P. da Luz
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Quiz - Random Networks

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Consider \( N = 4 \) nodes. Below are three sample outcomes of \( G(N, p) \) at different values of \( p \). Dashed lines show absent edges. Which graph is in the supercritical regime? (A) Graph A, because it has at least one edge and \( \langle k \rangle = 0.3 > 0 \) (B) Graph B, because \( \langle k \rangle = 1 \) satisfies the condition for the giant component (C) Graph C, because \( \langle k \rangle = 2.4 > 1 \), so \( p = 0.8 > p_c = 1/3 \) (D) All three are supercritical since every node has at least one neighbor (E) None of the above. Original idea by: Gustavo P. C. P. da Luz
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Quiz 1 - Clustering Coefficient

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 Consider the four graphs below: Which graph has the highest average clustering coefficient C, and what is its value? A) Graph 1, with C = 0 B) Graph 4, with C = 0.47 C) Graph 2, with C = 0.50 D) Graph 3, with C = 0.10 E) None of the above Original idea by: Gustavo P. C. P. da Luz
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