1. A distributed database system for a communication network having a plurality of nodes, each of which nodes includes a distributed database, said distributed database system comprising: local process means for extracting relations from each database of said communication network by performing local processes at each of said nodes of said communication system when a query including multi-attribute relations is input from one of said nodes; degree setting means for setting a degree number of each of said extracted relations from said local process means based on (A) tuple numbers of single-attribute relations derived from said multi-attribute relations and (B) a tuple number of each of said multi-attribute relations; relation set means for arranging a plurality of relation sets, each of which relation sets contains relations having the same degree number in ascending order by grouping said extracted relations from said local process means according to the degree number set by said degree setting means, wherein said relation sets include a first relation set containing relations with the lowest degree number; extraction means for extracting single-attribute relations from each of said relation sets arranged by said relation set means so that said single-attribute relations are added to said first relation set; semijoin operating means for repeatedly semijoining two relations of a relation set when a quantity of transfer data after said semijoining is detected to be smaller than a quantity of transfer data before said semijoining, and for adding derived relations resulting from said semijoining to a following relation set among the plurality of relation sets arranged by said relation set means; and control means or allowing said semijoin operating means to sequentially perform said semijoining and said adding for all of the plurality of relation sets arranged by said relation set means, starting from said first relation set and ending at a relation set having the highest degree number, so that each derived relation resulting from said semijoining is added to the transfer data.