# CS 765: Complex Networks

## Fall 2017

## Network Lab 1

## Due on Thursday Sep 20 at 1 pm

**Network Basics** (2 points)

Go to the site http://www.visualcomplexity.com.
Select and list two projects describing a network.
Answer the following about them (this may require going into the source webpage for the project, linked to from the visualcomplexity site).

- What do the nodes and edges represent?
- Is the graph directed? Weighted?
- Can the data be represented as a bipartite graph?

**Graph Theory** (8 points)

From the Network Science book

**Complete 2.12.3: Graph Representation**

The adjacency matrix is a useful graph representation for many analytical calculations. However, when we need to store a network in a computer, we can save computer memory by offering the list of links in a Lx2 matrix, whose rows contain the starting and end point i and j of each link. Construct for the networks (a) and (b) in Image 2.20:

(a): The corresponding adjacency matrices.

(b): The corresponding link lists.

(c): Determine the average clustering coefficient of the network shown in Image 2.20a.

**Complete 2.12.4: Degree, Clustering Coefficient and Components**

(a): Consider an undirected network of size N in which each node has degree k = 1. Which condition does N have to satisfy? What is the degree distribution of this network? How many components does the network have?

(b): Consider now a network in which each node has degree k = 2 and clustering coefficient C = 1. How does the network look like? What condition does N satisfy in this case?

**Complete 2.12.5: Bipartite Networks**

Consider the bipartite network of Image 2.21

(a): Construct its adjacency matrix. Why is it a block-diagonal matrix?

(b): Construct the adjacency matrix of its two projections, on the purple and on the green nodes, respectively.

(c): Calculate the average degree of the purple nodes and the average degree of the green nodes in the bipartite network.

(d): Calculate the average degree in each of the two network projections. Is it surprising that the values are different from those obtained in point (c)?

**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.