1. A trigger query obtaining apparatus comprising: a memory; and a processor operatively connected to the memory, the processor being programmed to: create a minimal directed graph, the minimal directed graph being a smallest directed graph unit having at least two nodes and a link connecting the at least two nodes, the link being directed from one of the at least two nodes to another one of the at least two nodes a direction of the link being created based on satisfying one of: a common-click condition based on a most frequent search criteria, a common-click condition based on a character-string extension criteria a common-click condition based on a best search criteria a common-query condition, or a common-user condition, each of the nodes corresponding to a search query, each search query including at least one keyword, each search query being included in at least two search logs, each of the at least two search logs including identical web page identification information identifying a web page selected by a user in search results for a search query included in each search log, each search query being used for a search to obtain a web page; calculate a score of each node of a directed graph, which is composed of a plurality of minimum directed graphs including the created minimum directed graph, the score of each node of the directed graph including the created minimal directed graph being calculated by propagating the score of each of the nodes from a seed query, based on a link analysis for relevance to the seed query, the link analysis being performed by weighting each node of the directed graph, the seed query being a query including a keyword belonging to a specific category; obtain and store in the memory a trigger query, the trigger query being a search query corresponding to one of the nodes of the directed graph having a calculated score that satisfies a predetermined condition, the trigger query including a keyword corresponding to a category identical to the specific category of the keyword included in the seed query; output the obtained trigger query; receive a new query from a terminal device, the new query being a query including a keyword to be used for a search; output the search results based on the new query; obtain and output, in response to the new query matches one of the trigger queries stored in the memory, a dedicated search result of a trigger-query-dedicated search for a category of a keyword included in a seed query used to obtain the matched trigger query; and accumulate a trigger query in the memory.