Maximum-Entropy Networks by Tiziano Squartini & Diego Garlaschelli

Author:Tiziano Squartini & Diego Garlaschelli
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

By contrast, the agreement improves substantially under the RCM: now, all the z-scores (with the only exception of motif 8) lie within the error bars . This indicates that, once the number of reciprocated and non-reciprocated links of each node are separately controlled for, the triadic structure of the network is almost completely explained. Moreover, the shape of the profiles is more stable than under the DCM. All these findings indicate that the RCM should be preferred to the DCM, the reciprocity structure playing a strong role in shaping the topology of the WTW [23, 25].

The panels of Fig. 3.10 also show the significance profiles for all 13 motifs, as defined in Eq. (3.27). We find that discounting the effect of the increasing size of the network makes the curves of the 6 different snapshots collapse to a single profile. This effect is obviously more evident under the DCM, since under the RCM the z-scores of the different snapshots were already largely overlapping.

So, even if in absolute terms many structural quantities change (the number of nodes, the number of links, the degrees, etc.), under both null models the significance profiles are extremely stable, clearly pointing out that the deviating patterns are systematic and the relative importance of each motif remains constant.

We now show the results of the reciprocity analysis of the WTW is almost completely consistent with a quasi-equilibrium network driven by the local (non-)reciprocated degrees , and . In other words, even if the network undergoes major changes under the effect of complicated economic and political processes (such as the creation of new independent states, globalization and the establishment of reciprocated relationships), once these processes are reabsorbed into the evolution of the local constraints, the quasi-equilibrium character of the network becomes manifest.

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