51. On the limit value of compactness of some graph classes.
- Author
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Lokot, Tatiana, Mehler, Alexander, and Abramov, Olga
- Subjects
- *
DISCONNECTED graphs , *HYPERMEDIA , *HYPERTEXT systems , *GEOMETRIC vertices , *GEODESIC distance - Abstract
In this paper, we study the limit of compactness which is a graph index originally introduced for measuring structural characteristics of hypermedia. Applying compactness to large scale small-world graphs (Mehler, 2008) observed its limit behaviour to be equal 1. The striking question concerning this finding was whether this limit behaviour resulted from the specifics of small-world graphs or was simply an artefact. In this paper, we determine the necessary and sufficient conditions for any sequence of connected graphs resulting in a limit value of CB = 1 which can be generalized with some consideration for the case of disconnected graph classes (Theorem 3). This result can be applied to many well-known classes of connected graphs. Here, we illustrate it by considering four examples. In fact, our proof-theoretical approach allows for quickly obtaining the limit value of compactness for many graph classes sparing computational costs. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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