Random Dot Product Graph Sampler
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A Latent Position Graph is a type of random graph model where vertices are associated with positions in some latent (unobserved) space. The Random Dot Product Graph (RDPG) is a Latent Position Graph. There are several definitions in the literature, but in this case we define it as a model where every vertex is associated with a vector of magnitude less than or equal to 1. The dot product of two vectors becomes the probability of an edge between the two associated vertices. Because probabilities are positive, we restrict the vectors to have all positive components. The latent space of a RDPG can be in any amount of dimensions, but for this program it is restricted to 3 dimensions for visualization purposes.
You can add vectors to the latent space by clicking on the surface of the light blue sphere. Scrolling your mousewheel on top of the plot will cause the radius of the light blue sphere to increase or decrease to allow you to add vectors in the entire octant. Clicking and dragging on the plot will allow you to view it from any angle. After you have added your latent positions click the "Sample Graph" button to view a graph that is sampled from the distribution created in the plot. The color of each node in the graph will correspond to the color of a point in the plot. The opacity of the links is related to the probability where lighter links indicate a smaller probability. When hovering over a node, its respective latent position point in the plot will increase in size. There is a collection of preset latent positions to use. The controls are listed below for convenience.