Fig S1: Validation of tERGM on synthetic networks from Temporal exponential random graph models of longitudinal brain networks after stroke
Creators: name: Obando, Catalina
name: Rosso, Charlotte
name: Siegel, Joshua
name: Corbetta, Maurizio
name: De Vico Fallani, Fabrizio
Publisher: name: The Royal Society
Year: 2022
Subjects: Computational Biology

description: S1A - Validation of temporal exponential graph models (tERGMs) in the case of relaxed temporal triangles on synthetic networks. A) Sequence of connectivity matrices representing a time-varying synthetic network. Unweighted and undirected networks are generated by a model that reproduces the large-scale reconfiguration changes after stroke. Interhemispheric integration and within-hemisphere segregation are obtained by allowing the formation of temporal edges <i>E</i> between blocks and temporal triangles T within blocks. Blocks (i.e. red squares) represent here two different systems, eg, the hemispheres (Material and methods). B) Cumulative counts of <i>E</i> and <i>T</i> between consecutive time steps for the synthetic temporal network. C) Prediction performance: area under the curve for the receiver operating characteristic (AUR, red curve) and precision recall (AUP, blue curve) of the out-of-sample link prediction in the networks simulated by the tERGM. Different curves correspond to different time steps. D) Validation: modularity <i>Q</i> values for i) the actual time-varying synthetic network (black line), ii) the ones simulated by the tERGM (green line), and iii) those simulated by a static version of the tERGM where the graph metrics were only accounting for the presence - not the formation - of edges and triangles (gray line).; S1B - Validation of tERGMs in the case of homogeneity violation. A) Sequence of connectivity matrices representing a time-varying synthetic network. The parameters to generate these networks were the same used for Fig. S3A. The only difference is that here the formation of temporal edges E and temporal triangles T are allowed only in the top block. Blocks (i.e. red squares) would represent here two different systems (eg, hemispheres). B) Cumulative counts of E and T between consecutive time steps for the synthetic temporal network. Because the rewiring process is now only taking place in one block the counts are lower compared to Fig. S3A; As a consequence, the corresponding parameter also become lower (θ_T=0.05 , θ_E=0.05). C) Prediction performance: area under the curve for the receiver operating characteristic (AUR, red curve) and precision recall (AUP, blue curve) of the out-of-sample link prediction in the networks simulated by the tERGM. Notice that the overall performance is higher here as compared to Fig. 2C. This is explained by the fact that the stability parameter introduced in the tERGM (see Eq. 5) is able to explicitly capture the homogeneity violation of the rewiring process. D) Validation: modularity Q values for i) the actual time-varying synthetic network (black line), ii) the ones simulated by the tERGM (green line), and iii) those simulated by a static version of the tERGM where the graph metrics were only accounting for the presence - not the formation - of edges and triangles (gray line).