9. One or more computer-storage memory devices having embodied thereon computer-executable instructions that, when executed, perform a method of improving a user's search experience on a search engine page using an entity data structure generated using breadcrumb elements from a plurality of Web pages, the method comprising: receiving at least a portion of a search query inputted by a user; accessing a data store that stores the entity data structure generated using the breadcrumb elements from the plurality of Web pages, wherein each breadcrumb element is part of a breadcrumb trail that represents a traversal path associated with each of the plurality of Web pages, the entity data structure in the form of a graph data structure having one or more root nodes, one or more parent nodes, and one or more child nodes; using the entity data structure, matching the at least the portion of the search query to a term in a breadcrumb element associated with a first child node in the entity data structure, the first child node having a first parent node; determining at least a second child node at the same structural level as the first child node, the second child node sharing a same root node as the first child node; identifying a second parent node associated with the at least the second child node, the second parent node being different from the first parent node; and presenting breadcrumb elements associated with the second parent node and the at least the second child node as at least one search item related to the at least the portion of the first search query on the search engine page, the at least one search item presented simultaneously with a set of algorithmic search results corresponding to the at least the portion of the search query, wherein the at least one search item is presented in a separate area than the set of algorithmic search results.
9. One or more computer-storage memory devices having embodied thereon computer-executable instructions that, when executed, perform a method of improving a user's search experience on a search engine page using an entity data structure generated using breadcrumb elements from a plurality of Web pages, the method comprising: receiving at least a portion of a search query inputted by a user; accessing a data store that stores the entity data structure generated using the breadcrumb elements from the plurality of Web pages, wherein each breadcrumb element is part of a breadcrumb trail that represents a traversal path associated with each of the plurality of Web pages, the entity data structure in the form of a graph data structure having one or more root nodes, one or more parent nodes, and one or more child nodes; using the entity data structure, matching the at least the portion of the search query to a term in a breadcrumb element associated with a first child node in the entity data structure, the first child node having a first parent node; determining at least a second child node at the same structural level as the first child node, the second child node sharing a same root node as the first child node; identifying a second parent node associated with the at least the second child node, the second parent node being different from the first parent node; and presenting breadcrumb elements associated with the second parent node and the at least the second child node as at least one search item related to the at least the portion of the first search query on the search engine page, the at least one search item presented simultaneously with a set of algorithmic search results corresponding to the at least the portion of the search query, wherein the at least one search item is presented in a separate area than the set of algorithmic search results. 14. The computer-storage memory devices of claim 9 , further comprising: using the entity data structure, matching the at least a portion of the search query to a term of a breadcrumb element associated with a parent node of the one or more parent nodes; determining one or more child nodes associated with the parent node; presenting breadcrumb elements associated with the parent node and the one or more child nodes as a query suggestion on the search engine page.