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:

Visualization Key


KV < 115
115<= KV <138
138<= KV <230
230<= KV <345
345<= KV <500
500<= KV

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.

This visualization is performed in Vis.js Copyright (C) 2010-2017 Almende B.V., dual licensed under Apache 2.0 and MIT