For my bachelors thesis I am working with tubifex worms, and trying to develop a graph theoretical model that can help explain some mechanical and dynamical properties of the worms once they have formed a "worm ball" (if you search up tubifex worms you can see what I mean).
We can define a "linking number" to represent how much two worms wrap/interact with each other. In the hypothetical graph model, we have the worms be nodes, and we link two nodes if they have a high enough linking number. From the data it seems as though the degree distribution in such a graph follows a power law, and I am trying to to see if I can simulate some kind of random graph to induce this distribution.
From my search through the internet and some literature, it seems as though for a graph to exhibit a power law degree distribution, continual adding of nodes needs to be part of the model. However in my case, I start off with a fixed amount of worms, and they somehow organize themselves into this worm ball.
My question is, are there any models that can replicate this behavior? The worm ball mechanics surely have some spatial/physical input, are there models that try to capture these things in other scenarios? I'm all ears for any suggestions.