The Structure Entropy of Social Networks

Micro triadic structure is an important motif and serves the building block of complex networks.In this paper,the authors define structure entropy for a social network and explain this concept by using the coded triads proposed by Davis and Leinhardt in 1972.The proposed structure entropy serves as a new macro-evolution index to measure the network’s stability at a given timestamp.Empirical analysis of real-world network structure entropy discloses rich information on the mechanism that yields given triadic motifs frequency distribution.This paper illustrates the intrinsic link between the micro dyadic/triadic motifs and network structure entropy.Importantly,the authors find that the high proportion of reciprocity and transitivity results in the emergence of hierarchy,order,and cooperation of online social networks.

Two-dimensional horizontal visibility graph analysis of human brain aging on gray matter

Characterizing the trajectory of the healthy aging brain and exploring age-related structural changes in the brain can help deepen our understanding of the mechanism of brain aging.Currently,most structural magnetic resonance imaging literature explores brain aging merely from the perspective of morphological features,which cannot fully utilize the grayscale values containing important intrinsic information about brain structure.In this study,we propose the construction of two-dimensional horizontal visibility graphs based on the pixel intensity values of the gray matter slices directly.Normalized network structure entropy(NNSE)is then introduced to quantify the overall heterogeneities of these graphs.The results demonstrate a decrease in the NNSEs of gray matter with age.Compared with the middle-aged and the elderly,the larger values of the NNSE in the younger group may indicate more homogeneous network structures,smaller differences in importance between nodes and thus a more powerful ability to tolerate intrusion.In addition,the hub nodes of different adult age groups are primarily located in the precuneus,cingulate gyrus,superior temporal gyrus,inferior temporal gyrus,parahippocampal gyrus,insula,precentral gyrus and postcentral gyrus.Our study can provide a new perspective for understanding and exploring the structural mechanism of brain aging.

Application research of multivariate linkage fluctuation analysis on condition evaluation in process industry

Abnormal conditions are hazardous in complex process systems, and the aim of condition recognition is to detect abnormal conditions and thus avoid severe accidents. The relationship of linkage fluctuation between monitoring variables can characterize the operation state of the system. In this study,we present a straightforward and fast computational method, the multivariable linkage coarse graining(MLCG) algorithm, which converts the linkage fluctuation relationship of multivariate time series into a directed and weighted complex network. The directed and weighted complex network thus constructed inherits several properties of the series in its structure. Thereby, periodic series convert into regular networks, and random series convert into random networks. Moreover, chaotic time series convert into scale-free networks. It demonstrates that the MLCG algorithm permits us to distinguish, identify, and describe in detail various time series. Finally, we apply the MLCG algorithm to practical observations series, the monitoring time series from a compressor unit, and identify its dynamic characteristics. Empirical results demonstrate that the MLCG algorithm is suitable for analyzing the multivariable linkage fluctuation relationship in complex electromechanical system. This method can be used to detect specific or abnormal operation condition, which is relevant to condition identification and information quality control of complex electromechanical system in the process industry.