# Adjacency matrices and network visualisations

• kcurse21
In summary, it seems that the adjacency matrices for these networks match, but it's not 100% certain and the dynamics are not yet known.
kcurse21
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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kcurse21 said:
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.
kcurse21 said:
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?

Mark44 said:
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.

## 1. What is an adjacency matrix?

An adjacency matrix is a mathematical representation of a network or graph. It is a square matrix where the rows and columns represent the nodes or vertices of the network, and the values in the matrix represent the connections or edges between the nodes.

## 2. How is an adjacency matrix used in network visualisations?

An adjacency matrix is commonly used to create visual representations of networks, such as graphs or diagrams. The matrix can be converted into a visual representation by assigning colors or shapes to the nodes and using the values in the matrix to determine the connections between the nodes.

## 3. What are the benefits of using an adjacency matrix for network visualisations?

One of the main benefits of using an adjacency matrix for network visualisations is that it allows for a clear and concise representation of complex networks. It also enables the identification of patterns and relationships within the network, which can aid in understanding the structure and dynamics of the network.

## 4. Are there any limitations to using adjacency matrices for network visualisations?

One limitation of using adjacency matrices is that they can become unwieldy for large networks, as the size of the matrix increases with the number of nodes. Additionally, they may not be the most suitable representation for certain types of networks, such as directed or weighted networks.

## 5. How can adjacency matrices be used in scientific research?

Adjacency matrices are commonly used in various fields of science, such as biology, sociology, and computer science, to study and analyze complex networks. They can be used to model and visualize relationships between genes, social interactions, or computer networks, among other applications.

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