Page rank

The page rank is a probability distribution over the vertices of the Webgraph $G = (V,E)$. This is a function $\pi : V \rightarrow [0,1]$ that assigns a ranking to each page. It is defined recursively as

$$\pi(x) = \sum_{y \in In(x)} \frac{\pi(y)}{\vert Out(y) \vert}.$$

With

• $Out(x) = \{y \in V \vert (x,y) \in E\}$, and
• $In(x) = \{y \in V \vert (y,x) \in E\}$.