Social Network Analysis - 2012 - 001

(via Coursera)


Asim Ihsan

Lecture notes

1A Why Social Network Analysis?

1B Software Tools

1C Degree and Connected Components

1D Gephi demo

2A Introduction to random graph models

2B: Random graphs and alternative models

2C: Models of network growth

3A: Centrality

\[ C_B(i) = /sum{j<k} \frac{g_jk(i)}{g_jk} \]

\[ C_B(i) = \frac{C_B(i)}{[(n-1)(n-2)/2]} \]

\[ C_c(i) = [\sum{j=1}^{N} d(i,j)]^(-1) \]

\[ C'_C(i) = \frac{C_C(i)}{(N-1)} \]

3B: Eigenvector and directed networks

c_i(\Beta) = \sum{j} (\alpha + \Beta c_j)A_(ji)

c(\Beta) = \alpha(I - \Beta A)^-1 \times A \times 1

\[ C'_B(i) = \frac{C_B(i)}{[(N-1)(N-2)]} \]

3C: Centrality applications (optional)

4A - Why detect communities?

4B - Heuristics for finding communities

4C - Community Finding

Q = 1/2m * sum(all pairs)[A_vw - k_v * k_w / 2m] * delta(c_v, c_w)


sum over all pairs of difference between adjacency matrix and probability of an edge between two vertices proportional to their degrees.

delta is 1 if in same community, using any metric you want, 0 if not.

5A - Small world experiments

5B - Clustering and motifs

5C - Small world models

5D - Origins of small worlds

6A: Network topology and diffusion

6B: Complex contagion

6C: Innovation in Networks

7A: Cool and unusual applications

7B: Predicting recipe ratings using ingredient networks

8A: Network resilience

8B: Resilience and assortativity

8C: Resilience and the power grid

e_path = [ sum_edges (1/e_edge) ] ^ -1

E = 1/(N_G N_D) * sum epsilon_ij for all paths ij.

epsilon_ij is efficiency of the most efficient path between i and j.

C_i = alpha * L_i(0), i = 1, 2, …, N.

8D: Concluding remarks


Week 4

Week 5

Week 7

Assignment notes

General notes