## 4 Results
### Networks & Regression Models  
By framing our outputs as networks of interactions between agents, the resultant networks shown in Figure 6 gain additional significance. Since much of the model mechanism of underlying agent rules was intentionally stochastic so would be our outputs. Nevertheless, non-random structure is evident and it can be presumed as having emerged from model rules. M1's match network produced a large component and many isolates, indicating that small preferences (in age for example) can produce clusters of nodes where there is high matching probability. The M2 match network showed highly dyadic structure (rather than transitive, as in in M1) suggesting that agents matched with one or two other agents, but not within larger clusters of agents as in M1. Interestingly, the like networks of both models are characterized by an even distribution of likes along a few large components with M2 also including many small isolates and isolated dyads. To ensure a principled comparison, we utilized the network regression technique--MRQAP [15]--to investigate the relationship of our monadic and dyadic covariates. MRQAP requires that we convert node attributes such as attractiveness, age, and ethnicity into difference (or similarity) adjacency matrices. Intended as a one-to-one comparison, the models in Table 8 included the 'like' network, attractiveness difference, age difference and ethnicity difference as independent/predictor variables and the'match' network as the dependent variable. We consider the effects of covariate inputs on producing a match as an output given the multiplicity of our two model types. Figure 6: Network visualizations of like network (top) for M1 (left) and M2 (right) and the equivalent Match Networks (bottom) where distinctive colors represent community detection by Louvain method [86]. (**A**) Like network of M1 agents showing roughly even distribution of likes with 3 components. (**B**) Like network of M2 agents showing many isolated dyads and one single large component. (**C**) Match network for M1 model with one large component, few smaller components and many isolated dyads. (**D**) Match network for M2 showing the disappearance of large components and the appearance of many smaller dyadic and triadic matches in small disparate communities. Reported are three models of interest--a single model describing M1 simulation results and two models for M2 simulation runs, the first of which is a model without an effect for messaging--a false model--the second of which (M2-T) includes the'message' network as an independent variable. Of note are the order of magnitude for all parameter estimates, which tend towards remarkably small values. For example, the M1 like relation estimate is 0.255; Assuming variable independence and given in absolute terms, it took roughly 4 likes to produce a match for M1 agents. This is in line with expectations about the density of the like network when compared to the density of the match network--the former expected to be more dense and the latter more sparse. Confidence in the reported parameter estimates is conveyed by the proportion of network permutations that meet lower-end one-tailed \(Pr(>=)\), upper-end one-tailed \(Pr(<=)\), and two-tailed tests \(Pr(>|=|)\). These reports communicate important features of the simulated systems. For example, 100% of the ensemble of networks permuted by M1 regression