PageRank

PageRank assigns importance scores to nodes in a directed network by modeling how links transmit influence. Its best-known use ranks web pages from their incoming links.

Random surfer model: A model of browsing in which a user follows links but occasionally jumps to a randomly chosen page. PageRank's link-following process is represented as a random surfer moving through the web.
Directed graph: A graph whose edges have direction, connecting an ordered source node to a destination node. Web links form the directed edges on which PageRank bases its scores.
Larry Page: An American computer scientist who co-founded Google and co-developed PageRank. His name is the source of the PageRank name, and he helped formulate the method.
Web search engine: A system that indexes web content and retrieves pages in response to queries. PageRank was developed to help order search results by the structure of web links.
Markov chain: A stochastic process whose next state depends only on its current state. Web navigation becomes a Markov chain whose long-run state probabilities yield PageRank scores.
Adjacency matrix: A matrix that records which pairs of graph nodes are connected by edges. It provides a compact representation of the links from which PageRank's transition probabilities are built.
Sergey Brin: A computer scientist who co-founded Google and co-developed its early search technology. He collaborated with Larry Page on the link-analysis method behind PageRank.
HITS algorithm: A link-analysis algorithm that scores web pages as hubs and authorities. It offers a related search-ranking approach with two scores rather than PageRank's single score.
Transition matrix: A matrix whose entries encode probabilities of moving between states in a stochastic process. Its link-derived probabilities specify how PageRank distributes score from one page to another.
Eigenvector centrality: A network centrality measure that assigns greater importance to nodes connected to important nodes. PageRank adapts this recursive notion of importance to directed links and random jumps.

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