Universal multilayer network exploration by random walk with restart

Abstract

The amount and variety of data have been increasing drastically for several years. These data are often represented as networks and explored with approaches arising from network theory. Recent years have witnessed the extension of network exploration approaches to capitalize on more complex and richer network frameworks. Random walks, for instance, have been extended to explore multilayer networks. However, current random walk approaches are limited in the combination and heterogeneity of networks they can handle. New analytical and numerical random walk methods are needed to cope with the increasing diversity and complexity of multilayer networks. We propose here MultiXrank, a method and associated Python package that enables Random Walk with Restart on any kind of multilayer network. We evaluate MultiXrank with leave-one-out cross-validation and link prediction, and measure the impact of the addition or removal of network data on prediction performances. Finally, we measure the sensitivity of MultiXrank to input parameters by in-depth exploration of the parameter space.

MultiCens: Multilayer network centrality measures to uncover molecular mediators of tissue-tissue communication

“…Beyond the field of biological networks, our measures represent an advance in the overall field of network centrality as well. For instance, compared to existing studies: (a) that are primarily based on either direct inter-layer interactions [20], or handle multi-hop connectivity but fail to distinguish between within-vs. across-layer interactions [7,21], MultiCens accounts for the multilayer multi-hop network connectivity structure of the underlying system; (b) on multiplex network centrality [14,[22][23][24], our MultiCens measures work for the more general class of multilayer networks (of which multiplex networks is a popular yet restricted sub-class); (c) on a RWR (Random Walk with Restart) based centrality score for each node of a heterogeneous or multilayer network [14,[25][26][27], we provide different informative MultiCens scores for each node at different global vs. local levels of granularity. For these reasons and the diverse applications we've demonstrated above, we believe our work on multilayer centrality opens up several future application areas in multi-organ systems-level modeling, a field that has been dominated so far by whole-body metabolic models [2] but onto which multi-organ gene network models like the ones proposed in this study can be integrated.…”

“….,L;i6 ¼j respectively as shown here and in Fig 1B . In this work, we assume our multilayer network to be undirected; thus M, A, C, and A [i,i] for each i are symmetric matrices. We also note here how this multilayer network model can also represent a heterogeneous network (such as those studied earlier [14,[25][26][27]30]). Heterogeneous network is a network model where different layers could've different node sets (e.g., a gene-disease heterogeneous network would've genes in the first layer and diseases in the second layer as nodes, and gene-gene, disease-disease, and inter-layer gene-disease links as edges).…”

“…RWR-H adapted for multilayer networks. RWR-H, a centrality measure based on the concept of Random Walk with Restart for a heterogeneous network, was originally proposed by Li and Patra [30] for a heterogeneous network model, and later adapted by [14,[25][26][27] for multiplex, heterogeneous and multiplex-heterogeneous network models. One way to define a representative RWR-H centrality is to closely follow Li and Patra's definition for a heterogeneous network, and adapt it to a multilayer network as given next.…”

“…Specifically, these existing methods utilize only the inter-layer degree of the nodes (S sec method [20]), or do not distinguish between withinlayer and across-layer connections (versatility method [21], key driver analysis [7]), or work with a popular yet restricted class of a multilayer network model called a multiplex network (wherein the only inter-layer edges allowed are those between the same node present in different layers) [14,[22][23][24], or do not delineate the local intra-layer vs. global inter-layer influence of nodes on other nodes in a multilayer network (or a closely related network model called a heterogeneous network). [14,[25][26][27].…”

Network-based integrative multi-omics approach reveals biosignatures specific to COVID-19 disease phases

“…We adapted multiXrank (83), a random walk with restart on a multilayer network algorithm to explore the disease-state omics-specific graphs. This algorithm was chosen because it enables random walk with restart on any kind of multilayer network generated from different data sources as compared to other methods that are limited in the combination and heterogeneity of networks that they can handle (29).…”