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Spectral centrality measures in temporal networks
Ars Mathematica Contemporanea. 2016. Vol. 11. No. 1. P. 11–33.
Batagelj V., Praprotnik S.
In our previous article we defined temporal quantities used for the description of temporal networks with zero latency and we showed that some centrality measures (e.g. degree, betweenness, closeness) can be extended to the case of temporal networks. In this article we broaden the scope of centrality measures in temporal networks to centrality measures derived from the eigenvectors of network matrices, namely the eigenvector in-centrality, the eigenvector out-centrality, the Katz centrality, the Bonacich α and (α, β)−centrality, the HITS algorithm (also known as Hubs and Authorities) introduced by Kleinberg, and the PageRank algorithm defined by Page and Brin. We extended our Python library TQ (Temporal Quantities) to include the algorithms from our research. The library is available online. The procedures will also be added to the user friendly program called Ianus. We tested the proposed algorithms on Franzosi’s violence network and on Corman’s Reuter terror news network and show the results
Levashev V., / Series arXiv "math". 2026. No. 2609.06010.
We prove that continuous A-bilinear pairings on the ring of Laurent series that are invariant under continuous automorphisms coincide, up to a constant, with the pairing given by the residue of a differential form over any commutative associative ring with identity. ...
Added: September 24, 2026
Pyatov P. N., Pivovarov P. A., / Series math "arxiv.org". 2026. No. 2609.06274.
We investigate a special ansats that allows for an iterative solution of the constant Yang-Baxter equation. Testing this ansatz, we construct four sequences of the constant R-matrices. In each sequence the R-matrices act on the tensor squares of vector spaces of linearly growing dimensions. Each R-matrix also depends on a single complex parameter.
By analyzing the ...
Added: September 24, 2026
Medvedev V., / Series arXiv "math". 2026.
We study complete static manifolds with boundary admitting a nowhere-vanishing static potential. Our main result shows that, under a natural lower bound relating the scalar curvature and the boundary mean curvature, a simple static manifold with boundary must in fact have positive scalar curvature, negative boundary mean curvature, and be compact; we also obtain explicit ...
Added: September 19, 2026
Poddiakov A., / Series Social Science Research Network "Social Science Research Network". 2026. No. 7437658.
Clarity of knowledge and reasoning is necessary in many cases. Yet vagueness in scientific thinking related to surprise, curiosity, "ability to engage with not-knowing" (de Freitas) and abductive reasoning is also a crucially important source of scientific creativity which supplements combinatorial logic when dealing with the already known. Starting from studies by C. S. Peirce ...
Added: September 15, 2026
Glutsyuk A., / Series arXiv "math". 2026.
B.Josephson (Nobel Prize, 1973) predicted a tunnelling effect for a system of two superconductors separated by a narrow dielectric (such a system is called Josephson junction): existence of a supercurrent through it and equations governing it. The overdamped Josephson junction is modeled by the family of differential equations on the 2-torus, dθdτ=1ω(cosθ+B+Acosτ), which is known as ...
Added: September 8, 2026
Pochinka O., Shmukler V., / Series math.RT "arXiv:1808.06395 [math.RT]". 2026.
Anosov flows have a long and rich history, firstly motivated by the
study of geodesic flows in negative curvature surface by Anosov and Sinai.
Not every closed manifold admits an Anosov flow for well-known reasons:
the fundamental group of a 3-manifold M admitting an Anosov flow must
have exponential growth, and M must be universally covered by R3. Nevertheless,
there ...
Added: August 31, 2026
Ustyuzhanin V., Zinkina J. V., Korotayev A., / Series "SocArXiv". 2026.
“Leaderlessness” is widely held to be a defining feature of contemporary mass mobilization, yet the claim rests on a handful of recent cases. We offer the first systematic cross-national analysis of this phenomenon from 1791 to 2019. We show that the absence of leadership is real but older and more modest than claimed: the share ...
Added: August 29, 2026
Loubenets E. R., / Series arxiv.org "quant-ph". 2026. No. 2607.18050.
In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general locality condition sufficient for a nonseparable Werner state with a ...
Added: July 21, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity.
To prove this, we study ...
Added: July 16, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...
Added: July 16, 2026
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
Added: June 11, 2026
Kravtsova M., Musaev A. U., Welzel C., / Series "SSRN Working Paper Series". 2026.
Elaborating on Welzel et al.'s "Cool Water Theory," our study zooms into the more limited (albeit still varied) framework conditions of Russia's huge territory. Within Russia's confines, we examine how the combination of moderately cool seasons with steady rain (i.e., Cool Water) affects sub-national areas' contemporary societal progress in two modernization indicators: material prosperity in ...
Added: June 3, 2026
Vorchik A., / SSRN. Серия Social Science Research Network "Social Science Research Network". 2026.
This work is devoted to a theoretical explanation of the Easterlin paradox, according to which long-term economic growth does not make average level of people's happiness increasing. By happiness, we mean the intensity of emotions people experience while comparing their new income with its expected value, or the target income with its original value. In the first case, ...
Added: May 31, 2026
Sizov A., Rodionova M., Sedashov E. et al., / NRU Higher School of Economics. Series PS "Political Science". 2026. No. 1.
Rapid development of surveillance technologies is one of the most socially important consequences of the digital age. This paper investigates the factors determining consent to surveillance of various types of personal data and contributes to rapidly growing research on citizens perceptions of surveillance practices. Relying on a comprehensive survey experiment, we study the effects of ...
Added: May 15, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Makarov I., Savchenko A., Arseny K. et al., PeerJ Computer Science 2022 Vol. 8 Article e858
Added: May 23, 2025
Makarov I., Savchenko A., Arseny Korovko et al., PeerJ Computer Science 2022 Vol. 8 Article e858
Many tasks in graph machine learning, such as link prediction and node classification, are typically solved using representation learning. Each node or edge in the network is encoded via an embedding. Though there exists a lot of network embeddings for static graphs, the task becomes much more complicated when the dynamic (i.e., temporal) network is analyzed. ...
Added: January 20, 2022
Batagelj V., Maltseva D., Journal of Informetrics 2020 Vol. 14 No. 1 P. 1–14
We present two ways (instantaneous and cumulative) to transform bibliographic networks, using the works’ publication year, into corresponding temporal networks based on temporal quantities. We also show how to use the addition of temporal quantities to define interesting temporal properties of nodes, links and their groups thus providing an insight into evolution of bibliographic networks. ...
Added: October 22, 2019
Shitov Y., Journal of Algebra 2017 Vol. 492 P. 393–401
Every (left) linear function on a subspace of a finite-dimensional vector space over a (skew) field can be extended to a (left) linear function on the whole space. This paper explores the extent to what this basic fact of linear algebra is applicable to more general structures. Semifields with a similar property imposed on linear ...
Added: January 30, 2019
Aleskerov F. T., Швыдун С. В., , in: Studies in Computational Intelligence* 1. Vol. 812: Complex Networks and Their Applications VII.: Springer, 2019. P. 94–103.
We propose a model that evaluates how much a network has changed over time in terms of its structure and a set of central elements. The difference of structure is evaluated in terms of node-to-node influence using known nodes correspondence models. To analyze the changes in nodes centralities we adapt an idea of interval orders ...
Added: December 4, 2018
CERINŠEK M., Batagelj V., , in: Encyclopedia of Social Network Analysis and Mining. 2nd Ed.: NY: Springer, 2017..
A network can be represented also with a corresponding matrix. Using matrix operations (addition and multiplication) over an appropriate semiring a unified approach to several network analysis problems can be developed. Matrix multiplication is about traveling on network. ...
Added: November 2, 2018
Batagelj V., PRAPROTNIK S., Social Network Analysis and Mining 2016 Vol. 6 No. 1 P. 1–22
n a temporal network, the presence and activity of nodes and links can change through time. To describe temporal networks we introduce the notion of temporal quantities. We define the addition and multiplication of temporal quantities in a way that can be used for the definition of addition and multiplication of temporal networks. The corresponding ...
Added: November 1, 2018
Shitov Y., Linear Algebra and its Applications 2016 Vol. 508 P. 225–233
Let R be a commutative semiring and S be an R-semimodule with inner product operation. A subset B ⊂ S is called standard orthogonal if, for any different b, c ∈ B, ⟨b, b⟩ is a unit and ⟨b, c⟩ = 0. Tan posed the following problem: Characterize semirings R such that, for every R-semimodule ...
Added: July 27, 2016