Assessing Low-Intensity Relationships in Complex Networks

Abstract

Many large network data sets are noisy and contain links representing low-intensity relationships that are difficult to differentiate from random interactions. This is especially relevant for high-throughput data from systems biology, large-scale ecological data, but also for Web 2.0 data on human interactions. In these networks with missing and spurious links, it is possible to refine the data based on the principle of structural similarity, which assesses the shared neighborhood of two nodes. By using similarity measures to globally rank all possible links and choosing the top-ranked pairs, true links can be validated, missing links inferred, and spurious observations removed. While many similarity measures have been proposed to this end, there is no general consensus on which one to use. In this article, we first contribute a set of benchmarks for complex networks from three different settings (e-commerce, systems biology, and social networks) and thus enable a quantitative performance analysis of classic node similarity measures. Based on this, we then propose a new methodology for link assessment called z* that assesses the statistical significance of the number of their common neighbors by comparison with the expected value in a suitably chosen random graph model and which is a consistently top-performing algorithm for all benchmarks. In addition to a global ranking of links, we also use this method to identify the most similar neighbors of each single node in a local ranking, thereby showing the versatility of the method in two distinct scenarios and augmenting its applicability. Finally, we perform an exploratory analysis on an oceanographic plankton data set and find that the distribution of microbes follows similar biogeographic rules as those of macroorganisms, a result that rejects the global dispersal hypothesis for microbes.

Homogeneous selection shapes free‐living and particle‐associated bacterial communities in subtropical coastal waters

“…The large input of freshwater is accompanied by heavy loading of nutrients, causing eutrophication, which is a major concern as it leads to the formation of a hypoxic bottom layer (Rabalais et al., 2009). The SCSPR is therefore a model system for studying threatened coastal ecosystems (Fennel & Testa, 2019), where changes in bacterial communities may precede detrimental effects on macroorganisms (Spitz et al., 2016).…”

Shannon entropy approach reveals relevant genes in Alzheimer’s disease

“…The network of co-expressed genes was built considering gene selected through the preprocessing procedure as nodes and analyzing their expressions for N = 31 subjects under investigation. In particular, given genes i and j , with expressions on the cohort { i a } a = 1,…, N and { j b } b = 1,…, N respectively, we computed the absolute value [24]: where r ij is the Pearson’s pairwise correlation: with and mean values of the two expression distributions. The result is adjacency matrix C , in which each elements c ij = f ( d ij ) is a function of the correlation between expressions of genes i and j and characterizes the strength of the corresponding link in the network.…”

A complex network approach reveals a pivotal substructure of genes linked to schizophrenia

“…Starting from the 85 gene expressions x i , i = 1, …, 85, and the 199 subjects selected, we measured the absolute value of Pearson’s pairwise correlations s ij to define the network of co-expressed genes [ 22 ]: We did not considered the sign of the correlation since we focused on the strength of the relationship between the pairs of genes, while we were not interested in the direction of such relationship [ 15 ]. Hence, we obtained ‘adjacency matrix A ’, where each elements a ij = f ( s ij ) is a function of the correlation measurements and measures the weight of the connection between two nodes of the network.…”