Modularity Calculations | That modularity optimization method relies on the maximization of a benefit function Q, which measures the difference between the number of connections within each module and the expected fraction of such connections given a “null model” , that is, a statistical model of random networks. |
Modularity Calculations | For undirected networks, the null model traditionally corresponds to random networks constrained to have the same degree sequence as the network whose modularity is measured. |
Modularity Calculations | Our results are qualitatively unchanged when using layered, feed-forward networks as “null model” to compute and optimize Q (Supp. |
Supporting Information | Two different null models for calculating the modularity score. |
Supporting Information | The conventional way to calculate modularity is inherently relative: one computes the modularity of network N by searching for the modular decomposition (assigning N’s nodes to different modules) that maximizes the number of edges within the modules compared to the number of expected edges given by a statistical model of random, but similar, networks called the “null model” . |
Supporting Information | Here, we calculated the modularity Q-score with two different null models , one modeling random, directed networks and the other modeling random, layered, feed-forward networks. |
Ordinary differential equation modeling | The second common method is known as the Likelihood-Ratio-Test (LRT), Where one model is defined as the null model and another nested model is compared against the null model [73]. |
Ordinary differential equation modeling | Here, the comparison is performed by where Adf denotes the difference in degrees of freedom of the null model and the nested model. |
Ordinary differential equation modeling | Hereby, one tests if a nested model is a valid simplification of the null model . |