ch5

Question 1

Degree, adjacency matrix, algebraic connectivity (AC)

Know what it is, and that AC is a measure of connectivity

Answer 1

Degree: Number of neighbours of a node (incoming edges)
Adjacency matrix (A): Matrix with 1 for connection and 0 for no connection
Algebraic connectivity: Second smallest eigenvalue of Q.
It can be used in analyzing the robustness and synchronizability of networks
Number of connected components in the graph / difficulty to disconnect

Question 2

Scale-free network
Know what it is, and understand why it is robust against
random failure but vulnerable against attacks

Answer 2

Scale free networks:
heterogeneous degree distribution: there is a huge variability between degrees, with several orders of magnitude between them
Big hubs
When nodes randomly fail, the largest part of the network is still operational
Whereas with an attack, the hubs can be targeted specifically to disrupt the network majorly

Question 3

Infection rate, curing rate

Know what it is

Answer 3

Infection rate:

• infection rate per link is beta
• An infected node can infect its neighbours with an infection rate beta

Curing rate:

• Curing rate per node is delta
• A node can be cured with a curing rate delta

Question 4

Effective spreading rate, and spectral radius

Know what these are, and how they are relation

Answer 4

Effective spreading rate:
Spreading rate:
- tau = beta / delta

When the spreading rate reaches a certain threshold tau c, the number of infected machines increases exponentially
 this threshold (tau c) = 1 / The spectral radius

Where the spectral radius is the largest eigenvalue of the Adjacency matrix.

Scale-free graphs have a much smaller spectral radius than for instance random graphs