Our Paper accepted to Nature Scientific Report !

Our paper entitled "Reliable Multi-Fractal Characterization of Weighted Complex Networks: Algorithms and Implications" has been accepted for publication in Nature Scientific Reports !

Through an elegant geometrical interpretation, the multi-fractal analysis quantifies the spatial and temporal irregularities of the structural and dynamical formation of complex networks. Despite its effectiveness in unweighted networks, the multi-fractal geometry of weighted complex networks, the role of interaction intensity, the influence of the embedding metric spaces and the design of reliable estimation algorithms remain open challenges.

To address these challenges, we present in this paper a set of reliable multi-fractal estimation algorithms for quantifying the structural complexity and heterogeneity of weighted complex networks. Our methodology uncovers that i) the weights of complex networks and their underlying metric spaces play a key role in dictating the existence of multi-fractal scaling and ii) the multi-fractal scaling can be localized in both space and scales.

In addition, this multi-fractal characterization framework enables the construction of a scaling-based similarity metric to connect to state-of-art machine learning framework for the identification of community structure of human brain connectome. The detected communities are accurately aligned with the biological brain connectivity patterns. This characterization framework has no constraint on the target network and can thus be leveraged as a basis for both structural and dynamic analysis of networks in a wide spectrum of applications.