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Cipriani, A. (author), Salvi, Michele (author)Assign to each vertex of the onedimensional torus i.i.d. weights with a heavytail of index τ−1>0. Connect then each couple of vertices with probability roughly proportional to the product of their weights and that decays polynomially with exponent α>0 in their distance. The resulting graph is called scalefree percolation. The goal of...journal article 2024
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Jonker, Stan (author)In this thesis, we examine the kernelbased spatial random graph (KSRG) model, which is a generalisation of many known models such as longrange percolation, scalefree percolation, the Poisson Boolean model and agebased spatial preferential attachment. We construct a KSRG from a vertex set V = Z^d, assigning each vertex v ∈ V a weight Wv...master thesis 2023
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Wassenaar, Vincent (author)A graph G=(V,E) is a mathematical model for a network with vertex set V and edge set E. A Random Graph model is a probabilistic graph. A Random Geometric Graph is a Random Graph were each vertex has a location in a space χ. We compare the ErdosRényi random graph, G(n,p), to the Random Geometric Graph model, RGG(n,r) where, in general we use r=c...bachelor thesis 2022
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Primavera, Alessandra (author)We consider the game cops and robbers, which is a pursuitevasion game played on a graph G. The cops and the robber take turns moving across the vertices of G, where the goal for the cops is to eventually catch the robber. Specifically, we study the cop number of G, i.e. the minimum number of cops that is needed to catch the robber on G. We...bachelor thesis 2022
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Morency, M.W. (author), Leus, G.J.T. (author)Graph signal processing is an emerging field which aims to model processes that exist on the nodes of a network and are explained through diffusion over this structure. Graph signal processing works have heretofore assumed knowledge of the graph shift operator. Our approach is to investigate the question of graph filtering on a graph about...journal article 2021
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Wang, R. (author)The random graph is a mathematical model simulating common daily cases, such as ranking and social networks. Generally, the connection between different users in the network is established through preference, and this phenomenon leads to a powerlaw behaviour of the degree sequence of the random graph. Other than studying this feature, the...master thesis 2020
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Gama, F. (author), Isufi, E. (author), Ribeiro, Alejandro (author), Leus, G.J.T. (author)Controllability of complex networks arises in many technological problems involving social, financial, road, communication, and smart grid networks. In many practical situations, the underlying topology might change randomly with time, due to link failures such as changing friendships, road blocks or sensor malfunctions. Thus, it leads to...journal article 2019
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Gama, F. (author), Isufi, E. (author), Leus, G.J.T. (author), Ribeiro, Alejandro (author)In this work, we jointly exploit tools from graph signal processing and control theory to drive a bandlimited graph signal that is being diffused on a random timevarying graph from a subset of nodes. As our main contribution, we rely only on the statistics of the graph to introduce the concept of controllability in the mean, and therefore...conference paper 2018
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Segarra, Santiago (author), Chepuri, S.P. (author), Marques, Antonio G. (author), Leus, G.J.T. (author)Stationarity is a cornerstone property that facilitates the analysis and processing of random signals in the time domain. Although timevarying signals are abundant in nature, in many contemporary applications the information of interest resides in more irregular domains that can be conveniently represented using a graph. This chapter reviews...book chapter 2018
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Bosma, Douwe (author)In this report the method of Markov chain Monte Carlo maximum<br/>likelihood estimation was used to estimate parameters in the Ising model<br/>and the exponential random graph model. The method and the models<br/>where described mathematically and problems that occurred during the<br/>estimation process where discussed. A package that executes...bachelor thesis 2017
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Isufi, E. (author), Loukas, A. (author), Simonetto, A. (author), Leus, G.J.T. (author)Graph filters play a key role in processing the graph spectra of signals supported on the vertices of a graph. However, despite their widespread use, graph filters have been analyzed only in the deterministic setting, ignoring the impact of stochasticity in both the graph topology and the signal itself. To bridge this gap, we examine the...journal article 2017
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Li, C. (author), Wang, H. (author), De Haan, W. (author), Stam, C.J. (author), Van Mieghem, P.F.A. (author)An increasing number of network metrics have been applied in network analysis. If metric relations were known better, we could more effectively characterize networks by a small set of metrics to discover the association between network properties/metrics and network functioning. In this paper, we investigate the linear correlation coefficients...journal article 2011
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Van Dijk, L.A. (author)This thesis consits of a literature study and an investigation of a new problem. This new problem involves a generalization of the (random graph) configuration model, the socalled alternative model.master thesis 2011
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Meibergen, N.J. (author)Beschouw een random graaf in het configuratiemodel. We analyseren de verdeling van het aantal lussen in een specifieke knoop wanneer het totaal aantal verbindingen, n, naar oneindig gaat. We onderscheiden daartoe drie situaties: de knoop heeft een eindig aantal, van de orde wortel n en van de orde n verbindingen.bachelor thesis 2011
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 Bhamidi, S. (author), Van der Hofstad, R. (author), Hooghiemstra, G. (author) journal article 2010
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Bhamidi, S. (author), Van der Hofstad, R. (author), Hooghiemstra, G. (author)We study first passage percolation (FPP) on the configuration model (CM) having powerlaw degrees with exponent ? ? [1, 2) and exponential edge weights. We derive the distributional limit of the minimal weight of a path between typical vertices in the network and the number of edges on the minimalweight path, both of which can be computed in...journal article 2010
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Dommers, S. (author), Van der Hofstad, R. (author), Hooghiemstra, G. (author)In this paper, we investigate the diameter in preferential attachment (PA) models, thus quantifying the statement that these models are small worlds. The models studied here are such that edges are attached to older vertices proportional to the degree plus a constant, i.e., we consider affine PAmodels. There is a substantial amount of...journal article 2010
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Van den Esker, H. (author), Van der Hofstad, R. (author), Hooghiemstra, G. (author)We generalize the asymptotic behavior of the graph distance between two uniformly chosen nodes in the configuration model to a wide class of random graphs. Among others, this class contains the Poissonian random graph, the expected degree random graph and the generalized random graph (including the classical ErdosRenyi graph). In the paper we...journal article 2008
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Van den Esker, H. (author)Many empirical studies on reallife networks show that many networks are small worlds, meaning that typical distances in these networks are small, and many of them have powerlaw degree sequences, meaning that the number of nodes with degree k falls off as kˆ (τ) for some exponent τ>1. These networks are modeled by means of scalefree random...doctoral thesis 2008