Let $\Gamma$ be the graph defined as follows:
- the vertices are mathematicians who have published papers
- there is an edge between any two mathematicians who have authored publications together.
Graph $\Gamma$ is certainly not connected, as there are mathematicians who have only published papers without collaborators. Obviously, the largest connected component is the one containing Paul Erdős, since almost all mathematicians today belong to this component. My question is:
Does anyone have an idea what the second-largest connected component is?