Original title: How Robust is Scale-Free Structure? Phase Transitions in Preferential Attachment Model under Attack?
Xiaoyun Gong, Gennady Samorodnitsky · September 2026
Networks like social media or the internet often grow through preferential attachment. This means popular points gain new connections faster, creating a scale-free network where a few hubs have tons of links. But what happens if an adversary attacks this growth? Researchers tested this using a growing network model where an attacker disrupts new links. At each step, a skilled attacker can stop a new edge from forming and instead delete an existing edge preferentially. The team found a sharp tipping point, called a phase transition. If the attacker's skill stays low, the network keeps its scale-free shape, though high-degree hubs weaken slightly. If the attacker's skill crosses a critical threshold, the scale-free structure is completely destroyed.
You are building a city where new roads always connect to the busiest intersections, so a few intersections become huge hubs. An attacker can sometimes stop a new road from being built and instead remove an existing road. If the attacker is weak, the city still has those huge hubs. But if the attacker is strong enough, the hub structure collapses. Here, the attacker's skill is the chance of blocking a new road and causing a deletion, and there is a tipping point where the network loses its hub-and-spoke pattern.
Many real networks, from the internet to social media, are scale-free, meaning a few nodes have many connections. This work shows that even a modest attacker can destroy that property if they are skilled enough, which has implications for network robustness and security. It reveals a tipping point where the network's fundamental structure changes.
The abstract doesn't say. It focuses on a theoretical model of attack on preferential attachment and describes the tail behavior of the degree distribution under different attacker skill levels. It does not discuss real-world networks, other attack strategies, or multiple attackers.
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How Robust is Scale-Free Structure? Phase Transitions in Preferential Attachment Model under Attack? — Xiaoyun Gong, Gennady Samorodnitsky
Abstract licence: CC0
Explanation generated by Synthesis from the abstract — it is not the original paper. This is a preprint, so it hasn't necessarily been peer reviewed.