Question 4 - Barabasi-Albert model

Question: Barabási- Albert model presents growth and preferential attachment. This raises two important questions are they really necessary? What happends in they absence?

I. They are not necessary. In their abscence nothing new happens.

II. They are not necessary. In the abscence of preferential attachment he model is forced to converge to a complete graph, fully connected and in the abscence of growth hubs are not present anymore, eliminating the scale-free characteristic. Those characteristicis are completely normal for this model.

III. They are necessary. In the abscence of preferential attachment he model is forced to converge to a complete graph, fully connected and in the abscence of growth hubs are not present anymore, eliminating the scale-free characteristic,

IV. They are necessary. In the abscence of preferential attachment hubs are not present anymore, eliminating the scale-free characteristic, and in the abscence of growth the model is forced to converge to a complete graph, fully connected.

Answer:

1. Only I is true.
   
   
2. Only II is true.
   
   
3. I and II are true.
   
   
4. Only IV is true.
   
   
5. None of the above

Question 3 - Scale-free networks

Question: Consider two scale-free networks. Both have γ equals 3 and the same kmax. The first one have N equals 144 and the second one N equals 100. If the first one have kmin of 100, what is the kmin of the second one?

Answer:

1. Kmax = 1.2
   
   
2. Kmax = 12
   
   
3. Kmax = 120
   
   
4. Kmax = 13
   
   
5. None of the above
   

Question 2 - Cayley Tree

Question: A Cayley tree is a symmetric tree, constructed starting from a central node.  What is the value of P, K and N for the one showed below?

Image from Network Science

Answer:

1. P = 5, K = 3, N = 94
   
   
2. P = 3, K = 5, N = 94
   
   
3. P = 4, K = 3, N = 96
   
   
4. P = 5, K = 2, N = 94
   
   
5. None of the above

Answer: A

Question 1 - Topological Sorting

Question:  There is a very complex process that can be optimized in a chip factory. All engineers decided to put together their knowledge and list where each part of this chip needs to be inserted, in order, to achieve the final assembly. Below you will find those dependecies, which graph best represents the overall process?

• Part 1: needs to be inserted into Part 2, then Part 4 and Part 5;
• Part 2: needs to be inserted into Part 4, then Part 5;
• Part 3: needs to be inserted only into Part 2;
• Part 4: needs to be inserted into Part 5;
• Part 5: does not have to be connected to anything;
• Part 6: needs to be inserted into Part 7;
• Part 7: needs to be inserted into Part 5;
• Part 8: needs to be inserted into Part 3;
• Part 9: needs to be inserted into Part 7.

Answer:

1. 
   
   
2. 
   
   
3. 
   
   
4. 

   
   
   
5. None of the above

Answer: B

About

This blog was created as a part of the course MO412/MC908 - Network Science ministred by João Meidanis.

There is also the course blog that can be accessed by clicking here.

This course is based on the book Network Science from Albert-László.