EE4C06 Networking
Summary of Slide Material & Exam tips
Dear student. Thank you for checking out this great summary! This is the result of many
weeks of hard work, collecting, refining and writing out all the stuff you need to know for
the exam! I (Timon) am an Embedded Systems master student at the TU Delft that finished
this course in October 2021. The course barely changes year by year since the professor
likes to do research more than to change his course, so this summary should be relevant for
many years to come!
At 32 pages, this summary is not very concise, but this is because this course is not very
concise! There is a lot to learn, but this document will help you greatly in the studying
process. This summary contains all the information you need, but unfortunatly you are NOT
able to pass the exam just by learning this. This document will aid you in remembering, but it
will not make you understand.
This course is more about understanding than about remembering, so please:
· Go to the lectures
· Ask questions if you don ‘t understand
· Practice with the excercises that are scattered throughout the slides (ctrl+f
‘excercise‘)
· Search wikipedia and the rest of the internet to learn the stuff you forgot (like all the
linear algebra that is part of this course, I really had to refresh that!)
Once you understand how the ideas work, and understand the stuff that is mentioned in the
slides, this document will help you to remember the rules, formulas, memory aids and
techniques to master the exam. But it does NOT replace the work that you have to do
yourself to understand what is happening.
How to use this document to gain the most from it
This document is set up in a specific way. To the left you see an empty column. In this
column, you can place an X when you are able to answer the prompt on the middle column
with the contents of the right column. This way, the document is a question/answer
document, that helps you connect ideas and concepts to their meaning.
1
, By placing an X when you know something, you indicate that you can answer the question
correctly (without looking at the answer, of course). Then, after you ‘ve gone through the
document for the first time, you can go through it again and skip all the items that you
marked. Then you go through it again, marking the items that you know, and then after
that you again skip the items that you marked! This will make sure that you focus your time
and energy on the stuff that needs your attention the most.
Once all items are marked, you ‘re done! Well, kind of. I do recommend to - after marking
all items, removing all X ‘s and studying until you have marked all items again at least once,
to double-check that you ‘ve got everything. But then you really should be done.
Contents of this document
This summary contains per lecture the most important ideas, formulas and definitions.
Furthermore, at the end of the document, I have included some very valuable tips that can
help you ace the exam! Be sure to check those out as well! I would even recommend to read
them before you start studying, so you know how to approach the process.
Good luck with studying, and don ‘t forget to have fun! ~Timon
X Lecture 1
two layers of a network – Topology/structure
– Service/function
property of both time-variant
which means... (Define it) A time-variant system is a system whose output response
depends on moment of observation as well as moment of input
signal application.
service is often designed.. independently of the topology
number of services per topology often more than 1
A graph consists of a set of _ that are – N nodes
connected by a set of _? – L links
Define the Königsberg Can one walk across the seven bridges and never traverse the
bridge problem same bridge twice?
Solution? does not exist
An Eulerian walk... visits each link in G once
An Eulerian walk exists if.. all nodes have even degree, and there are only zero or two
nodes with odd degree
2
,Define Topology domain
Define Spectral domain
(so basically: Matrices)
What is the value of the diagonal 0
entries of adjacency matrix
Define Geometric domain
What do we do for List of neighbors for each node, the set of direct neighbors is listed
in what order lexicographical order
which is... low to high alphabetically (a-z)
List of links representation is created · choose an ordering of links (e.g. lexicographic)
using the following two steps: · Each link l is defined by its end point nodes: l = i, j = j
etc.
Matrix A is an... Adjacency matrix
Adjacency matrix: what is columns, nodes are rows
what is rows? nodes are columns
when is an entry i, j = 1? i,j = 1 if there is an edge (i, j) in the graph G
Some things that are true for an – The degree of an arbitrary node i in the graph is the ith
adjacency matrix row sum of A
– The sum of its eigenvalues is 0
– The number of links in its graph is the sum of all entries
3
, DIVIDED BY TWO!
– The matrix is symmetric, which means that A = A^t, so
A(i, j) = A(j, i)
Matrix B is an... Incidence matrix
B: What is an incidence matrix? How is for each link there is a column, and the matrix describes where
it structured? each link comes from (row=+1) and where it goes to (row=-
1). So: The row sum of each row shows whether a node has
more outgoing(sum > 0) links or more incoming (sum<0) links
(or equal. Then sum = 0)
Memory aid: Think of it like water flowing from a high-
pressure place (1) to a low-pressure place (-1), or money
going from someone rich (1) to someone poor (-1).
same thing in krazy maths:
one EPIC AND DEEP thing that we can
derive from this OMG!!!
Or, in words: The sum
of entries in each column of the Incidence matrix B is always 0
Why is this deep? your mom is deep XD
All jokes aside, you can do some cool calculations with this
further on (expecially in lecture 5)
Delta (triangle) is a Degree matrix
Which shows? For each node how many connected edges it has
How is the degree matrix delta It is an NxN matrix with all the entries set to 0, except for the
structured? values on the diagonal. These are set to the degrees of node i.
So: delta(i, i) = degree of node i
Q is an... Laplacian matrix
How to calculate laplacian Q Diag(degrees) minus A. Here: Diag(degrees) means an empty
matrix with the degrees of a graph on the diagonal. This is
essentially the degree matrix.
The same in words Q = Diagonalized Degree matrix - Adjacency Matrix
B^t means Matrix B transposed
Since B*B^t is symmetric, so are... A and Q
So, which are the symmetric matrices? A, B*B^t and Q
trace sum of diagonal elements
What is the Trace of laplacian Q of Trace is sum of diagonal elements, diagonal elements are the
connected graph degrees and total of all degrees is 2*L, so 2L
So: Exlain what A, B, Delta and Q are – Adjacency matrix
– Indicence Matrix
4
