How to find connected components of a random graph?

How does pagerank work for disjoint connected components?

• I ran pagerank on a large graph. But, the graph is disjoint connected components. I have noticed that nodes in a small component received relatively high score, even though the number of nodes in the component is much smaller. Is this a disadvantage of PageRank? Are there workarounds for this?

• Answer:

  PageRank "fixes" this with the "teleportation" parameter, famously set to 0.15, that weakly connects all nodes to all other nodes. This can be thought of as an implicit link to all N other nodes in the graph with weight 0.15/N. Making this teleportation factor higher should allow a higher probability of escaping a small connected component. Without teleportation, PageRank does not provide a way to compare the centralities of nodes in different components. That is, computing the PageRank of a node tells you its relative importance *within that component*. But it does not tell you anything about how different components compare.