TY  - JOUR
AB  - 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 [1] 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 C_B = 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.
DA  - 2018
DO  - 10.1371/journal.pone.0207536
KW  - network theory
KW  - compactness of graphs
LA  - eng
IS  - 11
PY  - 2018
SN  - 1932-6203
T2  - PLOS ONE
TI  - On the limit value of compactness of some graph classes
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29321192
Y2  - 2024-12-26T21:26:16
ER  -