Hypergraph 3-node Subgraph CTMC

This project contains all code to replicate simulations in Hypergraph Modeling of the Evolution of Team Relationships with Applications to Academic Funding Collaboration by Ryan Haunfelder, Bailey Fosdick, and Haonan Wang.

Given holding parameters for the eight subgraphs, transition probabilities between them, and a viewing length, the triad_sim function generates a single observation from the CTMC model. The dyads and triads column give each state of the simulated chain. Each chain starts at the initial state h₀₀, so the first row will always have a dyad and triad value of 0.

lambda_true = c(1/250, 1/200, 1/200, 1/300, 1/300, 1/150 , 1/150)
names(lambda_true) = c("lambda00","lambda10","lambda20","lambda30","lambda01","lambda11","lambda21")

trans_probs_true = c(0.45, 0.45, 0.2, 0.45, 0.25, 0.3, 0.35, 0.35, 0.2, 0.3)
names(trans_probs_true) = c("p01|00","p10|00","p11|10","p20|10","p11|01",
                          "p21|11","p31|21","p31|30",
                          "p21|20","p30|20")
pars = c(lambda_true,trans_probs_true)

triad_sim(pars, 2000)

##   dyads triads TimeBetween  cumtime
## 1     0      0    489.7654 489.7654
## 2     0      1   1510.2346      Inf

The four simulation parameters are summarized in the table below.

	λ00	λ10	λ20	λ30	λ01	λ11	λ21
Simulation 1	250	200	200	300	300	150	150
Simulation 2	500	100	100	150	150	200	200
Simulation 3	200	100	100	150	400	450	450
Simulation 4	200	400	400	450	100	150	150

	p(h01|h00)	p(h10|h00)	p(h11|h10)	p(h20|h10)	p(h11|h01)	p(h21|h11)	p(h31|h21)	p(h31|h30)	p(h21|h20)	p(h30|h20)
Simulation 1	0.45	0.45	0.2	0.45	0.25	0.3	0.35	0.35	0.2	0.3
Simulation 2	0.1	0.3	0.35	0.6	0.9	0.9	0.8	0.8	0.25	0.65
Simulation 3	0.1	0.4	0.05	0.7	0.5	0.5	0.5	0.8	0.05	0.75
Simulation 4	0.6	0.2	0.6	0.1	0.7	0.7	0.7	0.6	0.5	0.4

The wireframe plots