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### Decomposition of graph to subgraphs according to parallel edges

I am supposed to calculate all-pair shortest path lengths of a graph. However, I first need the graph to be decomposed/expanded to a simple one based on the presence of parallel edges. If N parallel ...
1k views

### Intuition behind eigenvalues of an adjacency matrix

I am currently working to understand the use of the Cheeger bound and of Cheeger's inequality, and their use for spectral partitioning, conductance, expansion, etc, but I still struggle to have a ...
446 views

### How to generate random adjacency matrix with given number of components in graph

I am building a graph package in C and a part of the work involves generating a random graph with a given number of components in the graph. For example, if I wanted to generate a graph of 50 ...
38 views

### How to specify a robot go always right relative to itself from absolute perspective (north west east south)

I have a robot that has a start and goal position within a maze. Each point in the maze-grid is simply a Position object containing x and y. I need an algorithm that specifies the robot only moving to ...
53 views

I have created an adjacency matrix which looks something like this ...
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### Advantages (from a mathematical perspective) of representing data as symmetric matrices

From Wikipedia, a symmetric matrix is a square matrix that is equal to its transpose. An example of this (I think) is an adjacency matrix with undirected edges, which is a square matrix representing ...