Problem 1.
(a) Write down the adjacency matrix of network (a).
(b) Write down the cocitation matrix of network (a).
Problem 2
(a) Write down the incidence matrix of network (b).
(b) Write down the projection matrix for the projection of network (b) onto its black vertices.
Problem 3
Consider a bipartite network, with its two types of vertices. Suppose there are n1 vertices of type 1 and n2 vertices of type 2. Show that the mean degrees c1 and c2 of the two types are related by .
3
Problem 4.
Given
,
(a) Find all eigenvalues of matrix A.
(b) Find an orthogonal matrix U that diagonalizes A.
3
Problem 5.Read the tutorial from Ping-En Lu’s GitHub repository to install Python3 and python-igraph (if you need).
Paste your screenshots of “Hello, World!” of both Python 3 (5%) and python-igraph (5%), and write a brief report (5%). (For example, you can write down some problems you encountered, and how you solved them.)
Problem 6. Please download the tvshow dataset from Ping-En Lu’s GitHub repository, and find the following information from this dataset.
• Number of nodes.
• Number of edges.
• Mean degree.
• Maximum degree.
• Diameter.
You need to upload your python source code to eLearn, and write a brief report including screenshots, README file, and descriptions of your code below the solution area. There will be no points for this problem if you do not upload your python source code to iLMS.
