At any moment, the structure of a network is a graph, showing what nodes and edges are in the network, and how the nodes are interconnected by the edges. This graph is also called the topology of the network. The topology of a network may change with time. Depending on how the network topology changes, we can classify networks into three classes:
- Static networks. Static networks do not change their nodes and edges. More precisely, a network is a static network, if the node set and the edge set do not change over time.
- Dynamic networks. A dynamic network does not change its nodes, but may change its edges.
- Evolutionary networks. Evolutionary networks change both nodes and edges over time. An example is the network of all webpages on the World Wide Web. The node set (the set of all webpages) and the edge set (the set of Web links) both constantly change over time.
How Network Topology Helped Create Modern Search Engines
Early search engines computed search results by matching the key-words in search queries to the contents of webpages (nodes). These first-generation search engines only utilized nodes of the network of webpages.
Around 1996, Jon Kleinberg, Robin Li (李彦宏), and Larry Page, independently observed a phenomenon: Web links (edges) also significantly influence the relevance of search results. They utilized both nodes and edges to develop the second-generation search engines with much better results. This approach more fully utilizes network thinking and created Google and Baidu companies, serving billions of users and generating annual revenue over $100 billion.