Copying model

Copying model is a generative mechanism for network growth in which new nodes acquire their links by duplicating the connections of an existing node chosen at random. Unlike preferential attachment, where new nodes connect to high-degree nodes, the copying model produces power law degree distributions through a process of duplication and mutation: a new node copies most of the links of its chosen target, then adds or removes a few connections with some probability.

The copying model was introduced to explain the topology of the World Wide Web and biological networks where duplication is a plausible mechanism — gene duplication in protein interaction networks, and imitation in social systems. In the web context, a new webpage is created by an author who copies the links from an existing page they admire, then adds a few new ones. The result is a network with heavy-tailed degree distributions, high clustering, and rich community structure — properties that the simpler preferential attachment model struggles to reproduce simultaneously.

The copying model is mathematically related to Yule processes and Polya urn models, and it produces power-law exponents that depend on the copying fidelity and mutation rate. It is an example of how the same pattern — a power-law degree distribution — can emerge from fundamentally different generative processes, making the inverse problem of inferring mechanism from pattern particularly challenging in network science.

The copying model reveals that scale-free topology is not a signature of optimization or meritocracy. It is a signature of imitation. The hubs are not hubs because they are better; they are hubs because they were copied first. This has uncomfortable implications for how we interpret centrality in social and biological networks — what looks like importance may simply be historical accident amplified by duplication.