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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.
Background: Highlighted text in the Internet (i.e., hypertext) is predominantly blue and underlined. The perceptibility of these hypertext characteristics was heavily questioned by applied research and empirical tests resulted in inconclusive results. The ability to recognize blue text in foveal and parafoveal vision was identified as potentially constrained by the low number of foveally centered blue light sensitive retinal cells. The present study investigates if foveal and parafoveal perceptibility of blue hypertext is reduced in comparison to normal black text during reading.
Methods: A silent-sentence reading study with simultaneous eye movement recordings and the invisible boundary paradigm, which allows the investigation of foveal and parafoveal perceptibility, separately, was realized (comparing fixation times after degraded vs. un-degraded parafoveal previews). Target words in sentences were presented in either black or blue and either underlined or normal.
Results: No effect of color and underlining, but a preview benefit could be detected for first pass reading measures. Fixation time measures that included re-reading, e.g., total viewing times, showed, in addition to a preview effect, a reduced fixation time for not highlighted (black not underlined) in contrast to highlighted target words (either blue or underlined or both).
Discussion: The present pattern reflects no detectable perceptual disadvantage of hyperlink stimuli but increased attraction of attention resources, after first pass reading, through highlighting. Blue or underlined text allows readers to easily perceive hypertext and at the same time readers re-visited highlighted words longer. On the basis of the present evidence, blue hypertext can be safely recommended to web designers for future use.