Greedy triangular reduction:
no voltage threshold, degree threshold 8, random positions

Description of Reduction:

This is the visualization of the greedy triangular reduction performed to the degree two reduced network. We plot the smallest network produced in the experiment, under the degree threshold of 8 and without a voltage threshold for the permissible triangles. Initial positions in the visualization are randomly laid out. When the model is enabled, nodes are repelled from each other, but held together by springs (the edges between them). For a detailed description of the reduction process see our manuscript linked here.

Graph Labels:

• Coloring: nodes and edges are given color coding according the the highest voltage node included in this reduction. Edges without reduction share the color coding of their associated nodes.
• Generators: Generators are labelled with the "* MW" where * is number of megawatts for the generator.
• Super Nodes: Trees and triangles list the node number of the terminal node, the number of nodes in the reduction as "B**" where ** is the number of buses. The number of buses that are generators in the reduction are listed as "G***" where *** is the number of generators. If there are generators, the total megawatts of generation over all generators in the node "* MW" where * is the sum of the megawatts for each generator.
• Meta-edges: Meta-edges are labelled with E[B**,G*** *MW], with the same convention as above.

Visualization Key
Colors:
KV < 115	115<= KV <138	138<= KV <230	230<= KV <345	345<= KV <500	500<= KV	Generator
Node Symbols:		Terminal node collapsed tree			Terminal node collapsed triangle
Edge Symbols:		Edges with an arrow denote a meta-edge.

Description of Visualization Model:

The x and y coordinates for nodes in the network are distributed initially with a random seed upon each load of the page. The evolution of the nodes is governed by a repulsion attraction model in which nodes repulse and edges attract. Physics model for the visualization is set by default to the ForceAtlas2 Model and the solver is based partially on the equations provided in the model and the Barnes-Hut algorithm for n-body problems. A full description of the physics options is found in the Vis.js documentation, and summaries of the parameters are provided below. Note: the physics can be enabled or disabled with the button in the parameter slider

Parameter Descriptions
gravitationalConstant	This represents the gravitational constant for the attraction/ repulsion between nodes; the nodes are intended to repulse, so the constant is negative and if you want the repulsion to be stronger, decrease the value.
centralGravity	This parameter affects the strength of the central attractor for the system - when turned on, the gravity will pull the entire network towards the center with the same force irrespective of the distance from the center.
springLength	This parameter describes the rest length of the springs.
springConstant	This is a measure of spring stiffness, with higher values meaning stiffer springs
damping	The damping factor is how much of the velocity from the previous iteration of the physics simulation carries over to the next iteration.
avoidOverlap	When larger than 0, the size of the node is taken into account. The distance will be calculated from the radius of the encompassing circle of the node for both the gravity model. Value 1 is maximum overlap avoidance.
maximumVelocity	This limits the velocity the nodes can achieve in the simulation and slows down the stabilization of the model
minimumVelocity	This sets the threshold velocity that, if all nodes in the network fall under, the network is considered stabilized and the model stops.
solver	The solver is set by default to the forceAtlas2 model and in principle can be changed, but it is better to change the model for a fresh run within the options of the scripts.
timeStep	This sets the time step for the discretization of the physics; if it is too large the simulation will become unstable.