### The Diclique Representation and Decomposition of Binary RelationsThe Diclique Representation and Decomposition of Binary Relations

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 Author Haralick, Robert M. Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1974 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Abstract The binary relation is often a useful mathematical structure for representing simple relationships whose essence is a directed connection. To better aid in interpreting or storing a binary relation we suggest a diclique decomposition. A diclique of a binary relation $\textit{R}$ is defined as an ordered pair (I, O) such that $\textit{I}$ × $\textit{O}$ ⊆ $\textit{R}$ and (I, O) is maximal. In this paper, an algorithm is described for determining the dicliques of a binary relation; it is proved that the set of such dicliques has a nice algebraic structure. The algebraic structure is used to show how dicliques can be coalesced, the relationship between cliques and dicliques is discussed, and an algorithm for determining cliques from dicliques is described. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 1974-07-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 21 Issue Number 3 Page Count 11 Starting Page 356 Ending Page 366

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Source: ACM Digital Library