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Background: In bioinformatics, interactions are modelled as networks, based on graph models. Generally, these support a single-layer structure which incorporates a specific entity (i.e., node) and only one type of link (i.e., edge). However, real-world biological systems consisting of biological objects belonging to heterogeneous entities, and these operate and influence each other in multiple contexts, simultaneously. Usually, node similarities are investigated to assess the relatedness between biological objects in a network of interest, and node embeddings are widely used for studying novel interaction from a topological point of view. About that, the state-of-the-art presents several methods for evaluating the node similarity inside a given network, but methodologies able to evaluate similarities between pairs of nodes belonging to different networks are missing. The latter are crucial for studies that relate different biological networks, e.g., for Network Alignment or to evaluate the possible evolution of the interactions of a little-known network on the basis of a well-known one. Existing methods are ineffective in evaluating nodes outside their structure, even more so in the context of multilayer networks, in which the topic still exploits approaches adapted from static networks. In this paper, we presented pyMulSim, a novel method for computing the pairwise similarities between nodes belonging to different multilayer networks. It uses a Graph Isomorphism Network (GIN) for the representative learning of node features, that uses for processing the embeddings and computing the similarities between the pairs of nodes of different multilayer networks., Results: Our experimentation investigated the performance of our method. Results show that our method effectively evaluates the similarities between the biological objects of a source multilayer network to a target one, based on the analysis of the node embeddings. Results have been also assessed for different noise levels, also through statistical significance analyses properly performed for this purpose., Conclusions: PyMulSim is a novel method for computing the pairwise similarities between nodes belonging to different multilayer networks, by using a GIN for learning node embeddings. It has been evaluated both in terms of performance and validity, reporting a high degree of reliability., (© 2024. The Author(s).)

Background: Biological networks have proven invaluable ability for representing biological knowledge. Multilayer networks, which gather different types of nodes and edges in multiplex, heterogeneous and bipartite networks, provide a natural way to integrate diverse and multi-scale data sources into a common framework. Recently, we developed MultiXrank, a Random Walk with Restart algorithm able to explore such multilayer networks. MultiXrank outputs scores reflecting the proximity between an initial set of seed node(s) and all the other nodes in the multilayer network. We illustrate here the versatility of bioinformatics tasks that can be performed using MultiXrank., Results: We first show that MultiXrank can be used to prioritise genes and drugs of interest by exploring multilayer networks containing interactions between genes, drugs, and diseases. In a second study, we illustrate how MultiXrank scores can also be used in a supervised strategy to train a binary classifier to predict gene-disease associations. The classifier performance are validated using outdated and novel gene-disease association for training and evaluation, respectively. Finally, we show that MultiXrank scores can be used to compute diffusion profiles and use them as disease signatures. We computed the diffusion profiles of more than 100 immune diseases using a multilayer network that includes cell-type specific genomic information. The clustering of the immune disease diffusion profiles reveals shared shared phenotypic characteristics., Conclusion: Overall, we illustrate here diverse applications of MultiXrank to showcase its versatility. We expect that this can lead to further and broader bioinformatics applications., (© 2024. The Author(s).)

Compared with the general complex network, the multilayer network is more suitable for the description of reality. It can be used as a tool of network pharmacology to analyze the mechanism of drug action from an overall perspective. Combined with random walk algorithm, it measures the importance of nodes from the entire network rather than a single layer. Here a four-layer network was constructed based on the data about the action process of prescriptions, consisting of ingredients, target proteins, metabolic pathways and diseases. The random walk algorithm was used to calculate the betweenness centrality of the protein layer nodes to get the rank of their importance. According to above method, we screened out the top 10% proteins that play a key role in treatment. Prescriptions Xiaochaihu Decoction was taken as example to prove our method. The selected proteins were measured with the ones that have been validated to be associated with the treated diseases. The results showed that its accuracy was no less than the topology-based method of single-layer network. The applicability of our method was proved by another prescription Yupingfeng Decoction. Our study demonstrated that multilayer network combined with random walk algorithm was an effective method for pre-screening vital target proteins related to prescriptions., (Copyright © 2020 The Author(s). Published by Elsevier Inc. All rights reserved.)

We consider a Markovian SIR-type (Susceptible → Infected → Recovered) stochastic epidemic process with multiple modes of transmission on a contact network. The network is given by a random graph following a multilayer configuration model where edges in different layers correspond to potentially infectious contacts of different types. We assume that the graph structure evolves in response to the epidemic via activation or deactivation of edges of infectious nodes. We derive a large graph limit theorem that gives a system of ordinary differential equations (ODEs) describing the evolution of quantities of interest, such as the proportions of infected and susceptible vertices, as the number of nodes tends to infinity. Analysis of the limiting system elucidates how the coupling of edge activation and deactivation to infection status affects disease dynamics, as illustrated by a two-layer network example with edge types corresponding to community and healthcare contacts. Our theorem extends some earlier results describing the deterministic limit of stochastic SIR processes on static, single-layer configuration model graphs. We also describe precisely the conditions for equivalence between our limiting ODEs and the systems obtained via pair approximation, which are widely used in the epidemiological and ecological literature to approximate disease dynamics on networks. The flexible modeling framework and asymptotic results have potential application to many disease settings including Ebola dynamics in West Africa, which was the original motivation for this study.

Existing regionalization methods tend to be either spatial attribute- or spatial interaction-based, while real-world tasks usually involve both considerations to satisfy multiple objectives simultaneously. In this research, we propose Multilayer Network Community Detection and Kernel Extension (MNCD-KE), a two-step regionalization framework, as a feasible solution for such tasks. First, spatial attributes are embedded into attributes of nodes in a spatial interaction-defined multilayer network, and the kernel and marginal parts of the regions are determined by giving the membership value of the regionalization units to network communities. Second, the final result is obtained through a kernel extension process considering geographical constraints, including spatial contiguity, size balance, morphological regularity, and existing boundary consistency of the regions. Empirical experiments show that the proposed method yields outcomes that, in maintaining comparable performances with most baseline algorithms with either 'attribute' or 'interaction' objectives as measured by the respective criteria, simultaneously meet the dual objectives with results intuitively comprehensible. Its low computing costs and parameter adjustment flexibility make the proposed framework a convenient approach for real-world multi-objective regionalization tasks. We conclude the research with discussions on the boundary conditions for the framework to work and their relevance to city science theories, along with practical implications. [ABSTRACT FROM AUTHOR]

Analyzing the structures of multilayer networks (MLNs) has been a hot research topic in network science. Community detection algorithms are important tools for analyzing MLNs. In the literature, several community detection algorithms for MLNs have been proposed. Moreover, there are several options for the graph representation of an MLN: for example, directed or undirected, weighted or unweighted, and using information from all or only some layers. Although these options may affect the results of community detection in MLNs, representations that are effective for community detection have not yet been clarified. In this paper, we experimentally evaluate the effectiveness of three types of community detection algorithms for MLNs and examine how the graph representation of an MLN affects the results of these algorithms. Our main findings are as follows: (1) The flattening approach is particularly effective, whereas the layer-by-layer approach is not applicable to detecting communities in MLNs of Twitter users. (2) Using a directed graph for each layer of an MLN increases the accuracy of community detection. (3) The Leiden method, which is a community detection algorithm for single-layer networks, achieves comparable accuracy with the community detection algorithms for MLNs, which suggests that there exists room for improvement in multilayer community detection algorithms for effectively utilizing the multilayer structures of MLNs. [ABSTRACT FROM AUTHOR]

When collecting several data sets and heterogeneous data types on a given phenomenon of interest, the individual analysis of each data set will provide only a particular view of such phenomenon. Instead, integrating all the data may widen and deepen the results, offering a better view of the entire system. In the context of network integration, we propose the INet algorithm. INet assumes a similar network structure, representing latent variables in different network layers of the same system. Therefore, by combining individual edge weights and topological network structures, INet first constructs a Consensus Network that represents the shared information underneath the different layers to provide a global view of the entities that play a fundamental role in the phenomenon of interest. Then, it derives a Case Specific Network for each layer containing peculiar information of the single data type not present in all the others. We demonstrated good performance with our method through simulated data and detected new insights by analyzing biological and sociological datasets. [ABSTRACT FROM AUTHOR]

Network alignment (NA) is a popular research field that aims to develop algorithms for comparing networks. Applications of network alignment span many fields, from biology to social network analysis. NA comes in two forms: global network alignment (GNA), which aims to find a global similarity, and LNA, which aims to find local regions of similarity. Recently, there has been an increasing interest in introducing complex network models such as multilayer networks. Multilayer networks are common in many application scenarios, such as modelling of relations among people in a social network or representing the interplay of different molecules in a cell or different cells in the brain. Consequently, the need to introduce algorithms for the comparison of such multilayer networks, i.e., local network alignment, arises. Existing algorithms for LNA do not perform well on multilayer networks since they cannot consider inter-layer edges. Thus, we propose local alignment of multilayer networks (MultiLoAl), a novel algorithm for the local alignment of multilayer networks. We define the local alignment of multilayer networks and propose a heuristic for solving it. We present an extensive assessment indicating the strength of the algorithm. Furthermore, we implemented a synthetic multilayer network generator to build the data for the algorithm's evaluation. [ABSTRACT FROM AUTHOR]

The paper considers a Mixture Multilayer Stochastic Block Model (MMLSBM), where layers can be partitioned into groups of similar networks, and networks in each group are equipped with a distinct Stochastic Block Model. The goal is to partition the multilayer network into clusters of similar layers, and to identify communities in those layers. Jing et al. (2020) introduced the MMLSBM and developed a clustering methodology, TWIST, based on regularized tensor decomposition. The present paper proposes a different technique, an alternating minimization algorithm (ALMA), that aims at simultaneous recovery of the layer partition, together with estimation of the matrices of connection probabilities of the distinct layers. Compared to TWIST, ALMA achieves higher accuracy both theoretically and numerically. [ABSTRACT FROM AUTHOR]

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This paper is aimed at constructing robust multilayer networks against cascading failure. Considering link protection strategies in reality, we design a cascading failure model based on load distribution and extend it to multilayer. We use the cascading failure model to deduce the scale of the largest connected component after cascading failure, from which we can find that the performance of four kinds of load distribution strategies associates with the load ratio of the current edge to its adjacent edge. Coupling preference is a typical characteristic in multilayer networks which corresponds to the network robustness. The coupling preference of multilayer networks is divided into two forms: the coupling preference in layers and the coupling preference between layers. To analyze the relationship between the coupling preference and the multilayer network robustness, we design a construction algorithm to generate multilayer networks with different coupling preferences. Simulation results show that the load distribution based on the node betweenness performs the best. When the coupling coefficient in layers is zero, the scale-free network is the most robust. In the random network, the assortative coupling in layers is more robust than the disassortative coupling. For the coupling preference between layers, the assortative coupling between layers is more robust than the disassortative coupling both in the scale free network and the random network. [ABSTRACT FROM AUTHOR]

We present the algebraic representation and basic algorithms for MultiAspect Graphs (MAGs). A MAG is a structure capable of representing multilayer and time-varying networks, as well as higher-order networks, while also having the property of being isomorphic to a directed graph. In particular, we show that, as a consequence of the properties associated with the MAG structure, a MAG can be represented in matrix form. Moreover, we also show that any possible MAG function (algorithm) can be obtained from this matrix-based representation. This is an important theoretical result since it paves the way for adapting well-known graph algorithms for application in MAGs. We present a set of basic MAG algorithms, constructed from well-known graph algorithms, such as degree computing, Breadth First Search (BFS), and Depth First Search (DFS). These algorithms adapted to the MAG context can be used as primitives for building other more sophisticated MAG algorithms. Therefore, such examples can be seen as guidelines on how to properly derive MAG algorithms from basic algorithms on directed graphs. We also make available Python implementations of all the algorithms presented in this paper. [ABSTRACT FROM AUTHOR]

We consider network reliability in layered networks where the lower layer experiences random link failures. In layered networks, each failure at the lower layer may lead to multiple failures at the upper layer. We generalize the classical polynomial expression for network reliability to the multilayer setting. Using random sampling techniques, we develop polynomial-time approximation algorithms for the failure polynomial. Our approach gives an approximate expression for reliability as a function of the link failure probability, eliminating the need to resample for different values of the failure probability. Furthermore, it gives insight on how the routings of the logical topology on the physical topology impact network reliability. We show that maximizing the min cut of the (layered) network maximizes reliability in the low-failure-probability regime. Based on this observation, we develop algorithms for routing the logical topology to maximize reliability. [ABSTRACT FROM PUBLISHER]

As a more complicated network model, multilayer networks provide a better perspective for describing the multiple interactions among social networks in real life. Different from conventional community detection algorithms, the algorithms for multilayer networks can identify the underlying structures that contain various intralayer and interlayer relationships, which is of significance and remains a challenge. In this paper, aiming at the instability of the label propagation algorithm (LPA), an improved label propagation algorithm based on the SH-index (SH-LPA) is proposed. By analyzing the characteristics and deficiencies of the H-index, the SH-index is presented as an index to evaluate the importance of nodes, and the stability of the SH-LPA algorithm is verified by a series of experiments. Afterward, considering the deficiency of the existing multilayer network aggregation model, we propose an improved multilayer network aggregation model that merges two networks into a weighted single-layer network. Finally, considering the influence of the SH-index and the weight of the edge of the weighted network, a community detection algorithm (MSH-LPA) suitable for multilayer networks is exhibited in terms of the SH-LPA algorithm, and the superiority of the mentioned algorithm is verified by experimental analysis. [ABSTRACT FROM AUTHOR]