Fig 1.
Alternating k-star structures for modeling degree distribution in directed networks.
Alternating k-in-star models popularity spread and alternating k-out-star models activity spread.
Fig 2.
Alternating transitive k-triangle and alternating k-2-paths structures.
These are used for modeling social circuit dependence including path closure and shared popularity. The A2P-TD configuration counts k-2-paths (A2P-T) and shared popularity (A2P-D) configurations in a single configuration, adjusting for double counting.
Fig 3.
Binary attribute configurations.
The dark nodes represent actors with the binary attribute, and the lighter shaded nodes represent actors with or without the attribute.
Fig 4.
Categorical attribute configurations.
The filled and empty nodes represent actors with two different values of the categorical attribute.
Table 1.
Statistics of the simulated directed networks.
Fig 5.
Pokec network degree distribution.
Neither the in- nor the out-degree distribution are consistent with power law or log-normal distributions (p < 0.01).
Fig 6.
Pokec network degree distribution after hub nodes are removed.
After removing the 20 nodes that have in- or out-degree greater than 1000, the resulting network’s in-degree distribution is consistent with a power law distribution, but not with a log-normal distribution (p < 0.01). The out-degree distribution is consistent with neither a power law nor a log-normal distribution (p < 0.01).
Fig 7.
EstimNetDirected parameter estimates for 2000 node networks with categorical attribute.
The error bars show the nominal 95% confidence interval. The horizontal line shows the true value of the parameter, and each plot is also annotated with the mean bias, root mean square error (RMSE), the percentage of samples for which the true value is inside the confidence interval, the coverage (% in CI), and the Type II error rate (False Negative Rate, FNR). NC is the number of networks (of the total 100) for which a converged estimate was found, each of which is shown on the plot.
Fig 8.
EstimNetDirected parameter estimates for 2000 node networks with binary attribute.
The error bars show the nominal 95% confidence interval. The horizontal line shows the true value of the parameter, and each plot is also annotated with the mean bias, root mean square error (RMSE), the percentage of samples for which the true value is inside the confidence interval, the coverage (% in CI), and the Type II error rate (False Negative Rate, FNR). NC is the number of networks (of the total 100) for which a converged estimate was found, each of which is shown on the plot.
Table 2.
Results from estimation of simulated networks using EstimNetDirected estimating Type II error rate.
Table 3.
Results from estimation of full network using EstimNetDirected estimating Type I error rate.
Table 4.
Parameter estimates for the Pokec online social network with hubs removed.