Scale-free networks are types of networks characterized by a power-law distribution of node connectivity, meaning that a small number of nodes (or hubs) have a very high degree of connections, while most nodes have relatively few connections. This structure allows scale-free networks to be resilient to random failures but vulnerable to targeted attacks on the hubs. In the context of gene regulatory networks, these properties can help to explain how certain genes or proteins play central roles in regulating biological processes.
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