Using elements of both statistical inference and graph theory, this paper demonstrates how some properties of a complete network can be inferred by observing parts of it. The approach is considered especially beneficial when cost, time, or other constraints prohibit the collection of complete information on the network under consideration.
Get full access to this article
View all access options for this article.
References
1.
AbrahamC. T.GoshS. P., 1965, “Probability distributions for subgraphs of random graphs”, IBM Research Paper RC 1447.
2.
BloemenaA. R., 1964, Sampling from a Graph (The Netherlands Mathematics Centrum, Amsterdam).
3.
BurtonI., 1963, Accessibility in Northern Ontario: An Application of Graph Theory to a Regional Highway Network (Ontario).
4.
CapobiancoM. F., 1970, “Statistical inference in finite populations having structure”, Transactions of the New York Academy of Sciences, 32, Series 11, 401–413.
5.
CapobiancoM. F., 1972, “Estimating the connectivity of a graph”, in Graph Theory and Applications, Eds. AlaviY.LickD. R.WhiteA. T. (Springer-Verlag, Berlin).
6.
CapbiancoM. F., 1974, “Recent advances in stagraphics”, Annal of the New York Academy of Sciences, forthcoming.
7.
GartJ. J., 1970, “Some simple graphically oriented statistical methods for discrete data”, in Random Counts in Models and Structures, volume 1, Ed. PatilG. P. (Pennsylvania State University Press, University Park, Pa.).
8.
GoodI. J., 1950, Probability and the Weighing of Evidence (Charles Griffin, London).
9.
GoodI. J., 1965, The Estimation of Probabilities, Research Monograph 30 (MIT Press, Cambridge, Mass.).
10.
GoodmanL. A., 1961, “Snowball sampling”, Annals of Mathematical Statistics, 32, 148–170.
11.
JamesG. A.CliffA. D.HaggettP.OrdJ. K., 1970, “Some discrete distributions for graph with applications to regional transport networks”, Geografiska Annaler, 52B(1), 14–21.
12.
JaynesE. T. C., 1957, “Information theory and statistical mechanics”, Physics Review, 106, 620–630.
13.
KanskyK. J., 1963, “Structure of transport networks: Relationships between network geometry and regional characteristics”, Research Paper 84, Department of Geography, University of Chicago, Illinois.
14.
KatzL., 1951, “The distribution of the number of isolates in a social group”, Annals of Mathematical Statistics, 23, 271–276.
15.
KatzL.PowellJ. H., 1954, “The number of locally restricted directed graphs”, Proceedings of the American Mathematics Society, 5, 621–626.
16.
KatzL.PowellJ. H., 1957, “Probability distributions of random variables associated with a structure of the sample space of sociometric investigations”, Annals of Mathematical Statistics, 28, 442–448.
17.
KullbackS., 1968, Information Theory and Statistics (Dover Publications, New York).
18.
LavalleI. H., 1970, An Introduction to Probability, Decision, and Inference (Holt, Rinehart and Winston, New York).
19.
SavageL. J., 1962, “Bayesian statistics”, in Recent Developments in Information and Decision Processes, Eds. MacholR. E.GrayP. (Macmillan, New York).
20.
TapieroC. S.CapobiancoM. F.LewinA. Y., 1974, “Structural inference in large organizations”, Journal of Mathematical Sociology, forthcoming.
21.
TribusM., 1969, Rational Descriptions, Decisions and Designs (Pergamon Press, New York).
