THE PROBABILITY OF A GIVEN 1-CHOICE STRUCTURE.

Abstract

A 1-choice structure arises whenever each person in a group chooses exactly one other person according to some criterion. The purpose of the report is to study the situation in which these choices are made at random. Such a structure can be represented by a directed graph in which the points represent people and the directed lines their choices. The authors first describe the shape of such a 1-choice structure, and define its symmetry number. With the help of these properties they are then able to develop and prove a formula which gives a probability of obtaining a given structure in the random choice situation. In order to supply data for these results, they include in the Appendix the diagrams of all 1-choice structures with at most 6 points and the probability of each. Diagrams for 1-choice structures with 7 points were computed but are not included in the paper. (Author)

Document Details

Document Type
Technical Report
Publication Date
Feb 15, 1966
Accession Number
AD0643112

Entities

People

  • Frank Harary
  • Ron Read

Organizations

  • University of the West Indies

Tags

DTIC Thesaurus Topics

  • Behavior And Behavior Mechanisms
  • Behavioral Disciplines And Activities
  • Behavioral Sciences
  • Continents
  • Cooperation
  • Geographic Regions
  • Group Dynamics
  • Mathematics
  • Michigan
  • North America
  • Probability
  • Symmetry

Readers

  • Graph Algorithms and Convex Optimization.
  • Systems Analysis and Design