General Information¶

**Due Date:** 18.02.2015 23:59 <br >
**Late submission policy:** -0.2 points per day <br >

Please send your reports to mailto:[email protected] and mailto:[email protected] with message subject of the following structure:<br > **[HSE Networks 2015] {LastName} {First Name} HA{Number}**

Support your computations with figures and comments. <br > If you are using IPython Notebook you may use this file as a starting point of your report.<br > <br >

<hr >

Consider Barabasi and Albert dynamical grow model. Two main ingredients of this model are *network growing* and *prefferential attachment*. Implement two restricted B&A-based models:
<br >

**Model A**
<br >
Lack of prefferential attachment, that is at each time-step form edges uniformly at random while network keeps growing.

**Model B**
<br >
Lack of growing, that is fix total number of nodes, on each time-step randomly choose one and form edges with prefferential attachment.
<br >

- Generate networks according to the models above ($N > 1000$ nodes)
- Compute CDF/PDF, describe the distribution and compute\describe its properties.
- Illustate the following dependencies:
- average path length to the number of nodes
- average clustering coefficient to the number of nodes
- average node degee to the nodes "age"

- Is scale-free property conserved in these models?

Analyse results with respect to various parameter settings

Task 2¶

Consider the following "Vertex copying model" of growing network.

At every time step a random vertex from already existing vertices is selected and duplicated together with all edges, such that every edge of the vertex

- is copied with probability $q$
- is rewired to any other randomly selected vertex with probability $1-q$

Starting state is defined by some small number of randomly connected vertices.

The model can generate both directed and undirected networks.

- Generate graphs based on the model ($N > 1000$ nodes)
- Compute CDF/PDF, describe the distribution and compute\describe its properties.
- Illustate the following dependencies:
- average path length to the number of nodes
- average clustering coefficient to the number of nodes
- average node degee to the nodes "age"

Analyse results with respect to various parameter settings