  Complex networks have certain properties that distinguish them from their
respective uniform or regular counterparts. One of these properties is the
variation of topological properties along different hierarchical levels. In
this work, we study how networks that are constructed by repeatedly
incorporating a given motif exhibit this property. A motif is henceforth
understood as a small subgraph with a reference node where the incorporation
respectively occurs. We generate fractal networks using different motifs and
observe how their topology changes depending along the growth stages. Two
regimes are respectively identified: transient and equilibrium. The former is
characterized by significant topological changes that depend on the motif
topology, while the equilibrium regime shows more stable, parallel
trajectories. A more systematic analysis revealed that the betweenness
centrality and the average shortest path lengths were the main topological
properties that change along the network growth.
