The most obvious way to define importance is with the influencer concept. Most influential nodes have many connections and, as such, are well placed to spread information. In the context of social networks, influencers often get offered advertising contracts with brands that want to harness their influencing power and let as many people as possible know about their products. With this in mind, nodes 3, 5, 6, and 9 in the previous diagram all have three connections, making them the most important nodes.
To go further and try to disentangle these four nodes, other methods have been proposed. The most famous of them is the PageRank algorithm, used by Google to rank the results of its search engine. PageRank updates the importance of a given node, taking into account the importance of its neighbors. If a web page has backlinks from an important page, its importance will increase, compared to another page that is referenced by less important pages...
