Motif-based functional backbone extraction of complex networks

As a natural abstraction of a large number of real-world systems, the structure and function of complex networks have been attracting increasing attentions in recent years. Existing studies have highlighted the statistical heterogeneity of connection patterns in large-scale networks, where valuable information is usually overwhelmed by redundant intricacy. In this case, the extraction of truly relevant nodes/connections of a large-scale network, namely, network backbones, can help form reduced but meaningful representations of a large-scale complex network and understand its fundamental structure and function. However, so far as we know, most existing backbone extraction methods focus mainly on the extraction of structural backbones, such as centrality-based backbones. Few studies have studied the problem of how to extract the functional backbones of a network, which is relevant to certain functional properties of the network. Accordingly, in this paper, we present two motif-based extraction methods to extract functional backbones of complex networks based on higher-order organization of salient motifs. One is built upon the global threshold method, and the other is based on the disparity filter method. We implement our proposed methods on a set of real-world networks to evaluate the performance. The results show that our extraction methods are more effective than other existing methods in terms of extracting functional backbones of a network, measured by motif centrality, motif degree, and motif abundance.