There exist several random graph models that are used
to model real life network because they tend to look
very similar to graphs you can find in many areas.

On example are preferential attachement graphs, in
particular the Barabasi-Albert model. It turns out
that, with high probability, such graphs do not belong
to any graph class for which nice meta-theorems are
known that guarantee efficient algorithms for a wide
variety of problems. Such problems are for example
all problems expressible in first-order logic and such
graph classes are for example classes with locally bounded
treewidth or nowhere-dense graphs.

We nevertheless can show that FO-model checking is
in FPT for Barabasi-Albert graphs.