Fig. 6: Re-analysis of Sampson’s Monastery networks using Multiscale Semiwalk Balance (MSB) approach.

Full spectra were used in computations (exact results). a Signed sociograms at times t = 2, 3, 4. Left side colors denote block membership according to the “ground truth” partition and right side colors correspond to MSB partitions. Positive ties are blue and negative are red. Individuals whose “ground truth” and MSB block memberships differ (Amand, Basil and John Bosco) as well as the leaders of Young Turks (John Bosco and Gregory) are labeled. Network layout was determined with the Kamada-Kawai algorithm using only positive ties with weights (distances) on cross-block ties rescaled by a factor of 5. b Time series of strong and weak Degree of Balance (DoB) measures for t = 1, …, 5 using MSB, denoted by \(B({\beta }_{\max })\) and \(W({\beta }_{\max })\) respectively, as well as strong DoB based on the Walk Balance (WB) approach of Estrada and Benzi⁴, which is equivalent to MSB approach with β = 1 using ordinary adjacency matrix (denoted by B(1)). c Weak local balance expressed as z-scores relative to the overall distribution. Points are sized proportionally to local contributions and ordered first by block membership and then by balance scores. Members who remained at the monastery after the culmination of the conflict (t = 5) are marked with red labels on the subplot for t = 4. d Time series of frustration ratios for t = 1, …, 5 according to partitions obtained with MSB and WB (β = 1) approaches as well as the “ground truth” solution (which is defined only for times t = 2, 3, 4). \({F}_{{{{{{{{\rm{MSB}}}}}}}}}^{U}\) denotes frustration values using the unweighted MSB approach.