Not all networks obey the scale-free law. While many real-world networks have been found to exhibit scale-free characteristics, there are also exceptions. Some networks might follow different types of degree distributions or may not have a power-law relationship between the node degree and its frequency.

Here are a few examples of networks that do not follow the scale-free law:

Erdős-Rényi random graphs: These graphs are generated by randomly connecting nodes with a fixed probability. They do not exhibit the power-law relationship characteristic of scale-free networks.

Regular graphs: Regular graphs are networks in which all nodes have the same degree. They also do not obey the scale-free law.

Bipartite graphs: Bipartite graphs consist of two disjoint sets of nodes, with edges connecting nodes between the two sets only. These graphs typically do not have a power-law degree distribution.

It's important to note that while the scale-free law has been observed in many complex networks, such as the Internet, social networks, and biological networks, not all networks conform to this pattern. The underlying mechanisms and properties of individual networks can lead to different topological structures and degree distributions. Therefore, it is essential to analyze each network's specific characteristics before drawing conclusions about its adherence to the scale-free law.