Spring embedding techniques attempt to visualize a network in a “natural” state. Typically, nodes are randomly placed in space, and edges are placed between nodes. Edges are modeled as springs, with attractive forces proportional to edge weights. A global repulsive force is added to the system, and an energetic cost is calculated. Nodes iteratively reposition, and the system is allowed to cool to an energetic minimum. Though local minima and multiple layout solutions are possible, the resulting visualizations conveniently represent the network structure, such that connected nodes tend to lie close to one another and far from nodes to which they have no edge. Though the technique is qualitative, it is much more accessible than examining adjacency matrices, and the complicated structures of networks with dozens to hundreds of nodes can be easily and quickly apprehended (Figure 3B). Additionally, though it is not actually necessary to visualize a network in order to understand it, visual inspection can facilitate an intuitive understanding of properties that may be quantified by other means. For example, Figure 3 shows the adjacency matrix and a
