Q1. (a) Briefly introduce how Force-directed algorithms encode networks. (b) In force-directed placement, does spatial proximity (visual clump) always indicate grouping/ community? Explain. (c) One of the weakness of force-directed placement is that the layouts are often nondeterministic. What does it mean? (d) Illustrate the scalability issue of force-directed placement briefly. Q2. (a) How does adjacency matrix encode networks? (b) Give an example of matrix view of a network that’s not from the textbook and explain what it is. You need to include the reference if the answer is found online. Q3. (a) How does treemaps encode trees? (b) Given an example of Treemap layout that’s not from the textbook and explain what it is. You need to include the reference if the answer is found online. Q4. Color can be best understood in terms of three separate channels: luminance, hue, and saturation. Briefly explain how does this system specify colors. (Figures can be used to help illustration.) Q5. Explain the meaning of HSL /HSV and how does this system specify colors? Q6. (a) What are three major problems with the common continuous rainbow colormap? (b) Is there any way to address these three problems? Explain how.

Q1. Force-directed algorithms are used to visualize networks by simulating the physical forces between nodes. These algorithms assign forces to the nodes and then iteratively update the positions of the nodes based on these forces. The forces are typically based on concepts such as attractive forces between connected nodes and repulsive forces between all nodes.

In force-directed placement, spatial proximity does not always indicate grouping or community. This is because the force-directed algorithms aim to find an arrangement of nodes that minimizes overall forces, rather than grouping related nodes together. As a result, nodes may be positioned close to each other due to attractive forces, but this does not necessarily mean they belong to the same group or community.

One weakness of force-directed placement is that the layouts generated by these algorithms are often nondeterministic. This means that running the same force-directed algorithm multiple times with the same input can produce different layout results. This is because the iterative process involves random initialization and the simulation of physical forces, making the outcome sensitive to the initial conditions and the order in which the nodes are considered.

Scalability is another issue with force-directed placement. Force-directed algorithms can become computationally expensive as the number of nodes and edges in the network increases. The time complexity of these algorithms is typically O(n^3), where n is the number of nodes. As a result, generating layouts for large networks can be time-consuming and may require optimization techniques or approximations to improve performance.

Q2. Adjacency matrix is a way to encode networks by representing the connections between nodes using a matrix. In an adjacency matrix, the rows and columns correspond to the nodes in the network, and the entries in the matrix indicate whether there is an edge between two nodes.

For example, consider a network with nodes A, B, C, and D. An adjacency matrix for this network would be:

A B C D
A 0 1 1 0
B 1 0 0 1
C 1 0 0 1
D 0 1 1 0

In this matrix, a value of 1 indicates the presence of an edge between two nodes, while a value of 0 indicates no edge. For instance, there is an edge between nodes A and B, but no edge between nodes A and D. The adjacency matrix provides a compact representation of the network’s connectivity.

Q3. Treemaps are a space-filling visualization technique used to encode hierarchical data structures such as trees. In a treemap, the nodes of the tree are represented as rectangles, and the size of each rectangle is proportional to some attribute of the corresponding node.

For example, consider a treemap representing file sizes in a directory. Each rectangle in the treemap corresponds to a file, and its size represents the file’s size. The rectangles are positioned and sized in a way that partitions the available space in a hierarchical manner, reflecting the directory structure.

A specific example of a treemap layout is the “Squarified Treemap,” which aims to create rectangles with a more square-like shape to improve readability. This technique, pioneered by Mark Bruls, Kees Huizing, and Jarke van Wijk, optimizes the aspect ratio of the rectangles while ensuring space efficiency. It is often used to visualize hierarchical data in various domains, such as file systems, organizational structures, and financial data.