Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA Tensor-Based Framework for Studying Eigenvector Multicentrality in Multilayer Networks
286
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Centrality is widely recognized as one of the most critical measures to provide insight in the structure and function of complex networks. While various centrality measures have been proposed for single-layer networks, a general framework for studying centrality in multilayer networks (i.e., multicentrality) is still lacking. In this study, a tensor-based framework is introduced to study eigenvector multicentrality, which enables the quantification of the impact of interlayer influence on multicentrality, providing a systematic way to describe how multicentrality propagates across different layers. This framework can leverage prior knowledge about the interplay among layers to better characterize multicentrality for varying scenarios. Two interesting cases are presented to illustrate how to model multilayer influence by choosing appropriate functions of interlayer influence and design algorithms to calculate eigenvector multicentrality. This framework is applied to analyze several empirical multilayer networks, and the results corroborate that it can quantify the influence among layers and multicentrality of nodes effectively.
rate research
Read More
Recently, eigenvector localization of complex network has seen a spurt in activities due to its versatile applicability in many different areas which includes networks centrality measure, spectral partitioning, development of approximation algorithms and disease spreading phenomenon. For a network, an eigenvector is said to be localized when most of its components are near to zero, with few taking very high values. Here, we develop three different randomized algorithms, which by using edge rewiring method, can evolve a random network having a delocalized principal eigenvector to a network having a highly localized principal eigenvector. We discuss drawbacks and advantages of these algorithms. Additionally, we show that the construction of such networks corresponding to the highly localized principal eigenvector is a non-convex optimization problem when the objective function is the inverse participation ratio.
The spectral properties of the adjacency matrix, in particular its largest eigenvalue and the associated principal eigenvector, dominate many structural and dynamical properties of complex networks. Here we focus on the localization properties of the principal eigenvector in real networks. We show that in most cases it is either localized on the star defined by the node with largest degree (hub) and its nearest neighbors, or on the densely connected subgraph defined by the maximum $K$-core in a $K$-core decomposition. The localization of the principal eigenvector is often strongly correlated with the value of the largest eigenvalue, which is given by the local eigenvalue of the corresponding localization subgraph, but different scenarios sometimes occur. We additionally show that simple targeted immunization strategies for epidemic spreading are extremely sensitive to the actual localization set.
Networks are a convenient way to represent complex systems of interacting entities. Many networks contain communities of nodes that are more densely connected to each other than to nodes in the rest of the network. In this paper, we investigate the detection of communities in temporal networks represented as multilayer networks. As a focal example, we study time-dependent financial-asset correlation networks. We first argue that the use of the modularity quality function---which is defined by comparing edge weights in an observed network to expected edge weights in a null network---is application-dependent. We differentiate between null networks and null models in our discussion of modularity maximization, and we highlight that the same null network can correspond to different null models. We then investigate a multilayer modularity-maximization problem to identify communities in temporal networks. Our multilayer analysis only depends on the form of the maximization problem and not on the specific quality function that one chooses. We introduce a diagnostic to measure emph{persistence} of community structure in a multilayer network partition. We prove several results that describe how the multilayer maximization problem measures a trade-off between static community structure within layers and larger values of persistence across layers. We also discuss some computational issues that the popular Louvain heuristic faces with temporal multilayer networks and suggest ways to mitigate them.
There are different measures to classify a networks data set that, depending on the problem, have different success. For example, the resistance distance and eigenvector centrality measures have been successful in revealing ecological pathways and differentiating between biomedical images of patients with Alzheimers disease, respectively. The resistance distance measures the effective distance between any two nodes of a network taking into account all possible shortest paths between them and the eigenvector centrality measures the relative importance of each node in the network. However, both measures require knowing the networks eigenvalues and eigenvectors -- eigenvectors being the more computationally demanding task. Here, we show that we can closely approximate these two measures using only the eigenvalue spectra, where we illustrate this by experimenting on elemental resistor circuits and paradigmatic network models -- random and small-world networks. Our results are supported by analytical derivations, showing that the eigenvector centrality can be perfectly matched in all cases whilst the resistance distance can be closely approximated. Our underlying approach is based on the work by Denton, Parke, Tao, and Zhang [arXiv:1908.03795 (2019)], which is unrestricted to these topological measures and can be applied to most problems requiring the calculation of eigenvectors.
To improve the accuracy of network-based SIS models we introduce and study a multilayer representation of a time-dependent network. In particular, we assume that individuals have their long-term (permanent) contacts that are always present, identifying in this way the first network layer. A second network layer also exists, where the same set of nodes can be connected by occasional links, created with a given probability. While links of the first layer are permanent, a link of the second layer is only activated with some probability and under the condition that the two nodes, connected by this link, are simultaneously participating to the temporary link. We develop a model for the SIS epidemic on this time-dependent network, analyze equilibrium and stability of the corresponding mean-field equations, and shed some light on the role of the temporal layer on the spreading process.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
