In the early days, the standard approach of keyword search entailed typing in words or phrases into search engines and getting back a list of all the web pages that included that word or phrase. Web search is effectively a type of  pattern recognition that requires repeatedly redefining your search terms until you finally find something of interest. Which leads to the power of graph-based search.

Both Google and Facebook have since moved to graph databases that enhance search results with semantic search information gathered from a wide variety of sources. Graph systems understand the way data is related and hence offer a more precise and richer result. The key to their enhanced search capability is that the first search takes into account the entire structure of connected data available.

Graph-based search is also much quicker: you can query all of your connected data in real time, then hone in on the answers provided and launch new real-time searches prompted by the insights you have discovered.
Graph-based search is able to deliver relevant information that may not have been specifically asked for – offering a more proactive and targeted search experience that allows you to quickly triangulate onto the data points that are of the most interest to you.
It’s more of a natural ‘conversation’ with your data, rather than a series of one-off searches. It’s search and discovery, rather than search and retrieval.
If your business has large volumes of products or content, graph-based search provides a better way to make this data available to users.
Graph-based search offers numerous competitive advantages – including better customer experience, more targeted content, and increased revenue opportunities. And there are many areas where it is valuable, including customer support portals, content portals, product catalogs and social networks.
Graph databases can be 1,000 times faster than relational databases for working with connected data and graph-based search features can enable firms to discover new business insights, launch new products and services, and attract new customers.
Reference: http://go.neo4j.com/rs/710-RRC-335/images/Power-of-Graph-Based-Search.pdf