Social Network Analysis - 2012 - 001

(via Coursera)

 Student

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)

i.e.

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

Readings:

Week 4

Week 5

Week 7

Assignment notes

General notes