Adjacency matrices and network visualisations

  • #1
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Homework Statement:
Question is to match the matrices with the networks and describe the dynamics of the network.
Relevant Equations:
See provided picture.
I have this set of adjacency matrices and networks given to me and I need to match the matrix to the network and then describe the dynamics.

At first glance it seems to be Ac, Bb and Ca but I'm not sure if that's too obvious and I'm missing something as I haven't looked at visual representations of adjacency matrices before. Firstly, would I be correct in matching them?

Second, I need to briefly describe the dynamics of each network. For a short description of the networks: vertices correspond to the system state of a dynamical system, x(t), and edges exist if two dynamical states are close. I believe I need to choose from the following networks: regular, random, scale-free and small world.

My original guess was that a is small world and c is either random or scale free but I'm not sure. My second question is are these correct and what would b be?
 

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Answers and Replies

  • #2
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At first glance it seems to be Ac, Bb and Ca but I'm not sure if that's too obvious and I'm missing something as I haven't looked at visual representations of adjacency matrices before. Firstly, would I be correct in matching them?
For what it's worth, that would be my guess as well. Adjacency matrices that I've seen before were for connected graphs with a relatively small number of vertices.
My reasoning is that A is pretty solid with points, and that seems to match c. B is the least filled in, which seems to me to match b. C is not as dense as A, and a seems to be the best match.
Second, I need to briefly describe the dynamics of each network. For a short description of the networks: vertices correspond to the system state of a dynamical system, x(t), and edges exist if two dynamical states are close. I believe I need to choose from the following networks: regular, random, scale-free and small world.

My original guess was that a is small world and c is either random or scale free but I'm not sure. My second question is are these correct and what would b be?
No idea, as this network description stuff is new to me. Do you have any examples in your textbook or notes?
 
  • #3
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0
For what it's worth, that would be my guess as well. Adjacency matrices that I've seen before were for connected graphs with a relatively small number of vertices.
My reasoning is that A is pretty solid with points, and that seems to match c. B is the least filled in, which seems to me to match b. C is not as dense as A, and a seems to be the best match.
No idea, as this network description stuff is new to me. Do you have any examples in your textbook or notes?

Unfortunately I've looked through all my notes and worksheets and the only adjacency matrices I've done is with numbers, not visuals and the networks have all been in 2D and pretty simple. I don't have at textbook at all. I'll see if I can find some information on the types of networks and post it as well.
 

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