  Network motif analysis is a useful tool for the investigation of complex
networks. We study the profiles of tetradic motifs in horizontal visibility
graphs (HVGs) converted from multifractal binomial measures, fractional
Gaussian noises, and heartbeat rates. The profiles of tetradic motifs contains
the spatial information (visibility) and temporal information (relative
magnitude) among the data points in the corresponding time series. For
multifractal binomial measures, the occurrence frequencies of the tetradic
motifs are determined, which converge to a constant vector
$(2/3,0,8/99,8/33,1/99,0)$. For fractional Gaussian noises, the motif
occurrence frequencies are found to depend nonlinearly on the Hurst exponent
and the length of time series. These findings suggest the potential ability of
tetradic motif profiles in distinguishing different types of time series.
Finally, we apply the tetradic motif analysis to heartbeat rates of healthy
subjects, congestive heart failure (CHF) subjects, and atrial fibrillation (AF)
subjects. Different subjects can be distinguished from the occurrence
frequencies of tetradic motifs.
