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Register a new userTunable Eigenvector-Based Centralities for Multiplex and Temporal Networks
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Added by
Dane Taylor
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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Characterizing the importances (i.e., centralities) of nodes in social, biological, and technological networks is a core topic in both network science and data science. We present a linear-algebraic framework that generalizes eigenvector-based centralities, including PageRank and hub/authority scores, to provide a common framework for two popular classes of multilayer networks: multiplex networks (which have layers that encode different types of relationships) and temporal networks (in which the relationships change over time). Our approach involves the study of joint, marginal, and conditional supracentralities that one can calculate from the dominant eigenvector of a supracentrality matrix [Taylor et al., 2017], which couples centrality matrices that are associated with individual network layers. We extend this prior work (which was restricted to temporal networks with layers that are coupled by adjacent-in-time coupling) by allowing the layers to be coupled through a (possibly asymmetric) interlayer-adjacency matrix $tilde{{bf A}}$, where the entry $tilde{A}_{tt} geq 0$ encodes the coupling between layers $t$ and $t$. Our framework provides a unifying foundation for centrality analysis of multiplex and temporal networks; it also illustrates a complicated dependency of the supracentralities on the topology and weights of interlayer coupling. By scaling $tilde{{bf A}}$ by an interlayer-coupling strength $omegage0$ and developing a singular perturbation theory for the limits of weak ($omegato0^+$) and strong coupling ($omegatoinfty$), we also reveal an interesting dependence of supracentralities on the dominant left and right eigenvectors of $tilde{{bf A}}$.
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We describe centralities in temporal networks using a supracentrality framework to study centrality trajectories, which characterize how the importances of nodes change in time. We study supracentrality generalizations of eigenvector-based centralities, a family of centrality measures for time-independent networks that includes PageRank, hub and authority scores, and eigenvector centrality. We start with a sequence of adjacency matrices, each of which represents a time layer of a network at a different point or interval of time. Coupling centrality matrices across time layers with weighted interlayer edges yields a emph{supracentrality matrix} $mathbb{C}(omega)$, where $omega$ controls the extent to which centrality trajectories change over time. We can flexibly tune the weight and topology of the interlayer coupling to cater to different scientific applications. The entries of the dominant eigenvector of $mathbb{C}(omega)$ represent emph{joint centralities}, which simultaneously quantify the importance of every node in every time layer. Inspired by probability theory, we also compute emph{marginal} and emph{conditional centralities}. We illustrate how to adjust the coupling between time layers to tune the extent to which nodes centrality trajectories are influenced by the oldest and newest time layers. We support our findings by analysis in the limits of small and large $omega$.
Recent progress towards unraveling the hidden geometric organization of real multiplexes revealed significant correlations across the hyperbolic node coordinates in different network layers, which facilitated applications like trans-layer link prediction and mutual navigation. But are geometric correlations alone sufficient to explain the topological relation between the layers of real systems? Here we provide the negative answer to this question. We show that connections in real systems tend to persist from one layer to another irrespectively of their hyperbolic distances. This suggests that in addition to purely geometric aspects the explicit link formation process in one layer impacts the topology of other layers. Based on this finding, we present a simple modification to the recently developed Geometric Multiplex Model to account for this effect, and show that the extended model can reproduce the behavior observed in real systems. We also find that link persistence is significant in all considered multiplexes and can explain their layers high edge overlap, which cannot be explained by coordinate correlations alone. Furthermore, by taking both link persistence and hyperbolic distance correlations into account we can improve trans-layer link prediction. These findings guide the development of multiplex embedding methods, suggesting that such methods should be accounting for both coordinate correlations and link persistence across layers.
The modern age of digital music access has increased the availability of data about music consumption and creation, facilitating the large-scale analysis of the complex networks that connect music together. Data about user streaming behaviour, and the musical collaboration networks are particularly important with new data-driven recommendation systems. Without thorough analysis, such collaboration graphs can lead to false or misleading conclusions. Here we present a new collaboration network of artists from the online music streaming service Spotify, and demonstrate a critical change in the eigenvector centrality of artists, as low popularity artists are removed. The critical change in centrality, from classical artists to rap artists, demonstrates deeper structural properties of the network. A Social Group Centrality model is presented to simulate this critical transition behaviour, and switching between dominant eigenvectors is observed. This model presents a novel investigation of the effect of popularity bias on how centrality and importance are measured, and provides a new tool for examining such flaws in networks.
In network science complex systems are represented as a mathematical graphs consisting of a set of nodes representing the components and a set of edges representing their interactions. The framework of networks has led to significant advances in the understanding of the structure, formation and function of complex systems. Social and biological processes such as the dynamics of epidemics, the diffusion of information in social media, the interactions between species in ecosystems or the communication between neurons in our brains are all actively studied using dynamical models on complex networks. In all of these systems, the patterns of connections at the individual level play a fundamental role on the global dynamics and finding the most important nodes allows one to better understand and predict their behaviors. An important research effort in network science has therefore been dedicated to the development of methods allowing to find the most important nodes in networks. In this short entry, we describe network centrality measures based on the notions of network traversal they rely on. This entry aims at being an introduction to this extremely vast topic, with many contributions from several fields, and is by no means an exhaustive review of all the literature about network centralities.
Network alignment consists of finding a structure-preserving correspondence between the nodes of two correlated, but not necessarily identical, networks. This problem finds applications in a wide variety of fields, from the alignment of proteins in computational biology, to the de-anonymization of social networks, as well as recognition tasks in computer vision. In this work we introduce SPECTRE, a scalable algorithm that uses spectral centrality measures and percolation techniques. Unlike most network alignment algorithms, SPECTRE requires no seeds (i.e., pairs of nodes identified beforehand), which in many cases are expensive, or impossible, to obtain. Instead, SPECTRE generates an initial noisy seed set via spectral centrality measures which is then used to robustly grow a network alignment via bootstrap percolation techniques. We show that, while this seed set may contain a majority of incorrect pairs, SPECTRE is still able to obtain a high-quality alignment. Through extensive numerical simulations, we show that SPECTRE allows for fast run times and high accuracy on large synthetic and real-world networks, even those which do not exhibit a high correlation.
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