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).
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)?
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