# Modelling-graphs-with-linear-algebra

## Learning goals

1. Be able to read and build an adjacency matrix of a graph
2. Know some basic matrix vector multiplications to generate some statistics out of the adjacency matrix
3. Understand what is encoded in the components of the k-th power of the Adjacency matrix of a graph

## Script

The slide deck can be found at File:Linear Algebra for graphs.pdf

## Quiz

1 what information is encoded within the i-th row of the adjacency matrix?

 the pages linking to the i-th node the pages that are linked by the i-th node number of common neighbors with the i-th node the indegree distribution of the i-th node

2 Let ${\displaystyle A}$ be the adjacency matrix of a graph what information is stored in the components ${\displaystyle a_{ij}}$ of ${\displaystyle A^{k}}$?

 the number of paths that exist to go from node i to node j. the number of paths of length k that go from node i to node j. the number of paths of length up to k that go from node i to node j. the number of common neighbros between node i and node j. non of the above.

3 Let ${\displaystyle A}$ be the adjacency matrix of a graph and ${\displaystyle a_{ij}}$ be the components of ${\displaystyle A^{k}}$. Which of the following is true?

 if ${\displaystyle a_{ij}=0}$ then node i and j are in different connected components. if ${\displaystyle a_{ij}=0}$ then there is no path of length k connecting node i and node j. if ${\displaystyle a_{ij}=0}$ then there is no path of length shorter than k connecting node i and node j. there could be a path between node i and node j if k is bigger than the amount of vertices node i and node j are in two different connected components.

1. tba