  We model transport of individuals across a heterogeneous scale-free network
where a few weakly connected nodes exhibit heavy-tailed residence times. Using
the empirical law Axiom of Cumulative Inertia and fractional analysis we show
that `anomalous cumulative inertia' overpowers highly connected nodes in
attracting network individuals. This fundamentally challenges the classical
result that individuals tend to accumulate in high-order nodes. The derived
residence time distribution has a non-trivial U-shape which we encounter
empirically across human residence and employment times.
