# CS 491g/691g Special Topics on Social Networks

## Fall 2016

## Lab 2

## Due on Thursday Sep 29 at 1:00 pm

**Network Measures**

Excercise 3.7.1: Come up with an example of a directed connected graph in which eigenvector centrality becomes zero for some nodes. Describe when this happens.

Excercise 3.7.3: In PageRank, what α values can we select to guarantee that centrality values are calculated correctly (i.e., values do not diverge)?

Excercise 3.7.5: Consider a full n-tree. This is a tree in which every node other than the leaves has n children.
Calculate the betweenness centrality for the root node, internal nodes, and leaves.

Excercise 3.7.8(a): Find a graph with a minimum average clustering coeefficient when m = 15 and n = 10.

Excercise 3.7.10(a): Compute node similarity using Jaccard and cosine similarity for nodes v5 and v4.

**Submitting your files**
Submission of your homework is via WebCampus.
You must submit all the required files in a single pdf document containing all the answers.