Coarse graining for synchronization in directed networks

Motif-h: a novel functional backbone extraction for directed networks

Dense networks are very pervasive in social analytics, biometrics, communication, architecture, etc. Analyzing and visualizing such large-scale networks are significant challenges, which are generally met by reducing the redundancy on the level of nodes or edges. Motifs, patterns of the higher order organization compared with nodes and edges, are recently found to be the novel fundamental unit structures of complex networks. In this work, we proposed a novel motif h-backbone (Motif-h) method to extract functional cores of directed networks based on both motif strength and h-bridge. Compared with the state-of-the-art method Motif-DF and Entropy, our method solves two main issues which are often found in existing methods: the Motif-h reconsiders weak ties into our candidate set, and those weak ties often have critical functions of bridges in networks; moreover, our method provides a trade-off between the motif size and the edge strength, which quantifies the core edges accordingly. In the simulations, we compare our method with Motif-DF in four real-world networks and found that Motif-h can streamline the extraction of crucial structures compared with the others with limited edges.

Characteristics of Venture Capital Network and Its Correlation with Regional Economy: Evidence from China

Financial networks have been extensively studied as examples of real world complex networks. In this paper, we establish and study the network of venture capital (VC) firms in China. We compute and analyze the statistical properties of the network, including parameters such as degrees, mean lengths of the shortest paths, clustering coefficient and robustness. We further study the topology of the network and find that it has small-world behavior. A multiple linear regression model is introduced to study the relation between network parameters and major regional economic indices in China. From the result of regression, we find that, economic aggregate (including the total GDP, investment, consumption and net export), upgrade of industrial structure, employment and remuneration of a region are all positively correlated with the degree and the clustering coefficient of the VC sub-network of the region, which suggests that the development of the VC industry has substantial effects on regional economy in China.

Reconstructing propagation networks with temporal similarity

Node similarity significantly contributes to the growth of real networks. In this paper, based on the observed epidemic spreading results we apply the node similarity metrics to reconstruct the underlying networks hosting the propagation. We find that the reconstruction accuracy of the similarity metrics is strongly influenced by the infection rate of the spreading process. Moreover, there is a range of infection rate in which the reconstruction accuracy of some similarity metrics drops nearly to zero. To improve the similarity-based reconstruction method, we propose a temporal similarity metric which takes into account the time information of the spreading. The reconstruction results are remarkably improved with the new method.

Spectral coarse graining for random walks in bipartite networks

Many real-world networks display a natural bipartite structure, yet analyzing and visualizing large bipartite networks is one of the open challenges in complex network research. A practical approach to this problem would be to reduce the complexity of the bipartite system while at the same time preserve its functionality. However, we find that existing coarse graining methods for monopartite networks usually fail for bipartite networks. In this paper, we use spectral analysis to design a coarse graining scheme specific for bipartite networks, which keeps their random walk properties unchanged. Numerical analysis on both artificial and real-world networks indicates that our coarse graining can better preserve most of the relevant spectral properties of the network. We validate our coarse graining method by directly comparing the mean first passage time of the walker in the original network and the reduced one.