middle loops.","permanent magnet machine; Concentrated winding; eddy current losses; experimental validation","en","conference paper","IEEE","","","","","","","","","","DC systems, Energy conversion & Storage","","","" "uuid:bbae3221-ebdb-4a34-8dec-7f89546b2f22","http://resolver.tudelft.nl/uuid:bbae3221-ebdb-4a34-8dec-7f89546b2f22","Google-Earth Based Visualizations for Environmental Flows and Pollutant Dispersion in Urban Areas","Liu, D. (Shanghai Advanced Research Institute; University of Chinese Academy of Science); Kenjeres, S. (TU Delft ChemE/Transport Phenomena)","","2017","In the present study, we address the development and application of an efficient tool for conversion of results obtained by an integrated computational fluid dynamics (CFD) and computational reaction dynamics (CRD) approach and their visualization in the Google Earth. We focus on results typical for environmental fluid mechanics studies at a city scale that include characteristic wind flow patterns and dispersion of reactive scalars. This is achieved by developing a code based on the Java language, which converts the typical four-dimensional structure (spatial and temporal dependency) of data results in the Keyhole Markup Language (KML) format. The visualization techniques most often used are revisited and implemented into the conversion tool. The potential of the tool is demonstrated in a case study of smog formation due to an intense traffic emission in Rotterdam (The Netherlands). It is shown that the Google Earth can provide a computationally efficient and user-friendly means of data representation. This feature can be very useful for visualization of pollution at street levels, which is of great importance for the city residents. Various meteorological and traffic emissions can be easily visualized and analyzed, providing a powerful, user-friendly tool for traffic regulations and urban climate adaptations.","computational fluid dynamics; visualization; Google Earth; environmental pollution; KML","en","journal article","","","","","","","","","","","ChemE/Transport Phenomena","","","" "uuid:c9c93b5e-64aa-4889-b5b3-ebe012e2b8f1","http://resolver.tudelft.nl/uuid:c9c93b5e-64aa-4889-b5b3-ebe012e2b8f1","Comparison of Levelized Cost of Energy of a 10 MW superconducting and magnetic pseudo direct drive generator targeted for the INNWIND.EU reference turbine","Abrahamsen, Asger Bech (Technical University of Denmark); Liu, D. (TU Delft DC systems, Energy conversion & Storage); Magnusson, Niklas (SINTEF); Thomas, A (Siemens Wind Power); Z., Azar (Siemens Wind Power); Stehouwer, Ewoud (DNV-GL); Hendriks, E (Knowledge Centre WMC); Penzkofer, A. (University of Sheffield); Atallah, K (University of Sheffield); Dragan, R.R. (Magnomatics); .Clark, R.E. (Magnomatics); Deng, F. (Aalborg University); Chen, Z (Aalborg University); Karwatzki, D. (Leibniz Universität); Mertens, A. (Leibniz Universität); Parker, M. (University of Strathclyde); Finney, SJ (University of Strathclyde); Polinder, H.","","2017","Innovative drive trains targeted at 10-20 MW offshore turbines are investigated in the INNWIND.EU project in order to determine the impact on the Levelized Cost of Energy (LCoE) resulting when installed in the ,North sea at 50 m of water [1]. The two main technologies studied are superconducting direct drive (SCDD)[2] and the magnetic pseudo direct drive (PDD) [3] generators, which are both capable to providing compact drive trains with low weight and a small number of moving parts compared to a gearbox based drive train (see figure 1a). Superconducting field coils are used to provide the torque in the direct drive generators, where the armature windings are based on conventional copper wire and magnetic steel laminates operated at ambient temperature. Magnetic pseudo direct drive generators consist of a magnetic gearbox made of an inner free rotor (rotating at a geared up speed to the blade input) and an intermediate drive rotor inserted into an outer static armature winding, where the electricity is harvested.","","en","abstract","","","","","","","","","","","DC systems, Energy conversion & Storage","","","" "uuid:624e0a6f-854f-463b-be4c-62af81f363ad","http://resolver.tudelft.nl/uuid:624e0a6f-854f-463b-be4c-62af81f363ad","Finite Element Analysis and Experimental Validation of Eddy Current Losses in Permanent Magnet Machines with Fractional-Slot Concentrated Windings","Wang, X. (TU Delft DC systems, Energy conversion & Storage); Liu, D. (TU Delft DC systems, Energy conversion & Storage); Lahaye, D.J.P. (TU Delft Numerical Analysis); Polinder, H. (TU Delft DC systems, Energy conversion & Storage); Ferreira, J.A. (TU Delft Electrical Power Processing)","","2016","Permanent-magnet machines with fractional slot concentrated windings are easy to manufacture. Their popularity therefore is steadily increasing. Without a proper design, however, the induced eddy-current losses in the solid rotor get rather high. The modeling and the prediction of eddy-current losses for these machines are thus very important during the design process. This paper focuses on the finite-element analysis and the experimental validation of eddy-current losses for this kind of machine with a small axial length. Two-dimensional and three-dimensional transient finite-element models are developed for computing the eddy-current losses. The rotor motion is taken into account using an Arbitrary Lagrangian-Eulerian formulation. The total iron losses are measured experimentally and a method to separate the rotor iron losses from the total iron losses is presented. The validation results show that the twodimensional finite-element model overestimates the losses due to the end-effects being neglected. The three-dimensional model agrees much better with the measurements in both no-load and on-load operations.","Concentrated winding; eddy current losses; experimental validation; permanent magnet machine","en","conference paper","IEEE","","","","","","","","","","DC systems, Energy conversion & Storage","","","" "uuid:98088329-676a-4ba0-b76e-4dfb48e4eb4e","http://resolver.tudelft.nl/uuid:98088329-676a-4ba0-b76e-4dfb48e4eb4e","Short Circuits of a 10 MW High Temperature Superconducting Wind Turbine Generator","Song, X. (Technical University of Denmark); Polinder, H. (TU Delft DC systems, Energy conversion & Storage); Liu, D. (TU Delft DC systems, Energy conversion & Storage); Mijatovic, Nenad (Technical University of Denmark); Holbøll, Joachim (Technical University of Denmark); Jensen, Bogi Bech (University of the Faroe Islands)","","2016","Direct drive high temperature superconducting (HTS) wind turbine generators have been proposed to tackle challenges for ever increasing wind turbine ratings. Due to smaller reactances in HTS generators, higher fault currents and larger transient torques could occur if sudden short circuits happen at generator terminals. In this paper, a finite element model that couples magnetic fields and the generator’s equivalent circuits is developed to simulate short circuit faults. Afterwards, the model is used to study the transient performance of a 10 MW HTS wind turbine generator under four different short circuits, i.e., three-phase, phase-phase clear of earth, phase-phase-earth, and phase-earth. The stator current, fault torque, and field current under each short circuit scenario are examined. Also included are the forces experienced by the field winding under short circuits. The results show that the short circuits pose great challenges to the generator, and careful consideration should be given to protect the generator. The results presented in this paper would be beneficial to the design, operation and protection of an HTS wind turbine generator.","Finite element analysis; Force; High temperature superconducting generator; Short circuit; Transient","en","conference paper","IEEE","","","","","","","","","","DC systems, Energy conversion & Storage","","","" "uuid:942520af-7469-4fff-8893-40e007f52496","http://resolver.tudelft.nl/uuid:942520af-7469-4fff-8893-40e007f52496","An experimental and modelling evaluation of the deformation and fracture of quasi-brittle reticulated vitreous carbon foam","Heard, P; Šavija, B. (TU Delft Materials and Environment); Liu, D; Smith, GE; Hallam, KR; Schlangen, H.E.J.G. (TU Delft Materials and Environment); Flewitt, P.E.J.","Gdoutos, Emmanuel E. (editor)","2016","In quasibrittle materials the addition of specific microstructural features such as porosity can lead to departure from linear elastic behaviour prior to maximum force, followed by graceful failure. A simple but extreme example is reticulated vitreous carbon foam, with its opencell structure of brittle ligaments connected in a threedimensional array. Tensile testing has been made on foams with various pore and ligament dimensions to provide a measure of forcedisplacement, combined with acoustic monitoring, and evaluation of the associated elastic moduli and fracture strengths. These tests provide insights into the mechanisms of quasibrittle failure. The results are explored by comparing with predictions from a microstructurebased finite beam element model. Inputs to the model are the elastic modulus and fracture strength of the individual ligaments of the foam measured at the micro lengthscale. Results are discussed with respect to the energy of fracture, the distribution and progression of fracture for individual ligaments.","","en","conference paper","","","","","","","","","","","Materials and Environment","","","" "uuid:15757723-3ac7-4188-a489-4218436e2aa0","http://resolver.tudelft.nl/uuid:15757723-3ac7-4188-a489-4218436e2aa0","Multi-scale characterization and modelling of damage evolution in nuclear Gilsocarbon graphite","Liu, D.; Heard, P.; Savija, B.; Smith, G.; Schlangen, E.; Flewitt, P.","","2015","In the present work, the microstructure and mechanical properties of Gilsocarbon graphite have been characterized over a range of length-scales. Optical imaging, combined with 3D X-ray computed tomography and 3D high-resolution tomography based on focus ion beam milling has been adopted for microstructural characterization. A range of small-scale mechanical testing approaches are applied including an in situ micro-cantilever technique based in a Dualbeam workstation. It was found that pores ranging in size from nanometers to tens of micrometers in diameter are present which modify the deformation and fracture characteristics of the material. This multi-scale mechanical testing approach revealed the significant change of mechanical properties, for example flexural strength, of this graphite over the length-scale from a micrometer to tens of centimeters. Such differences emphasize why input parameters to numerical models have to be undertaken at the appropriate length-scale to allow predictions of the deformation, fracture and the stochastic features of the strength of the graphite with the required confidence. Finally, the results from a multi-scale model demonstrated that these data derived from the micro-scale tests can be extrapolated, with high confidence, to large components with realistic dimensions.","x-ray tomography; fracture; nuclear materials","en","conference paper","Materials Research Society","","","","","","","","Civil Engineering and Geosciences","Structural Engineering","","","","" "uuid:aabe6d90-0681-4139-9a6d-201e70843ead","http://resolver.tudelft.nl/uuid:aabe6d90-0681-4139-9a6d-201e70843ead","ILIGRA: An Efficient Inverse Line Graph Algorithm","Liu, D.; Trajanovski, S.; Van Mieghem, P.","","2014","This paper presents a new and efficient algorithm, ILIGRA, for inverse line graph construction. Given a line graph H, ILIGRA constructs its root graph G with the time complexity being linear in the number of nodes in H. If ILIGRA does not know whether the given graph H is a line graph, it firstly assumes that H is a line graph and starts its root graph construction. During the root graph construction, ILIGRA checks whether the given graph H is a line graph and ILIGRA stops once it finds H is not a line graph. The time complexity of ILIGRA with line graph checking is linear in the number of links in the given graph H. For sparse line graphs of any size and for dense line graphs of small size, numerical results of the running time show that ILIGRA outperforms all currently available algorithms.","graph algorithm; line graph; root graph","en","journal article","Springer","","","","","","","","Electrical Engineering, Mathematics and Computer Science","Network Architectures & Services (NAS)","","","","" "uuid:01387120-a39a-477f-acea-e5b902b018fa","http://resolver.tudelft.nl/uuid:01387120-a39a-477f-acea-e5b902b018fa","Design study of a 10 MW MgB2 superconductor direct drive wind turbine generator","Abrahamsen, A.B.; Magnusson, N.; Liu, D.; Stehouwer, E.; Hendriks, B.; Polinder, H.","","2014","A superconducting direct drive generator based on field windings of MgB2 superconducting tape is proposed as a solution by mounting the generator in front of the blades using a king-pin nacelle design for offshore turbines with power ratings larger than 10 MW as investigated in the INNWIND.EU project.","superconducting generator; direct drive generator; offshore wind turbine; nacelle integration","en","conference paper","EWEA","","","","","","","","Electrical Engineering, Mathematics and Computer Science","Electrical Sustainable Energy","","","","" "uuid:fabc0cb6-e868-4bf4-84c2-f45cfc7d6642","http://resolver.tudelft.nl/uuid:fabc0cb6-e868-4bf4-84c2-f45cfc7d6642","Design of an MgB2 race track coil for a wind generator pole demonstration","Abrahamsen, A.B.; Magnusson, N.; Jensen, B.B.; Liu, D.; Polinder, H.","","2014","An MgB2 race track coil intended for demonstrating a down scaled pole of a 10 MW direct drive wind turbine generator has been designed. The coil consists of 10 double pancake coils stacked into a race track coil with a cross section of 84 mm x 80 mm. The length of the straight section is 0.5 m and the diameter of the end sections is 0.3 m. Expanded to a straight section of 3.1 m it will produce about 1.5 T magnetic flux density in the air gap of the 10 MW 32 pole generator and about 3.0 T at the edge of the superconducting coil with an operation current density of the coil of 70 A/mm2.","","en","conference paper","IOP","","","","","","","","Electrical Engineering, Mathematics and Computer Science","Electrical Sustainable Energy","","","","" "uuid:42184015-8cac-4be2-8084-a221744d0452","http://resolver.tudelft.nl/uuid:42184015-8cac-4be2-8084-a221744d0452","Feasibility Study of a 10 MW MgB2 Fully Superconducting Generator for Offshore Wind Turbines","Kostopoulos, D.; Liu, D.; Genani, G.; Polinder, H.","","2013","Offshore wind is considered a vital component of the future large scale renewable generation portfolio. Intense R&D effort is occurring in both the technology and the supply chain aiming at cost reduction. The drivetrain of wind turbines is an area of continuous evolution with currently no one standard configuration in the industry. It is anticipated that in order to upscale offshore wind turbines in the 10+ MW power range innovation is necessary in this subsystem. A possible solution could be the adoption of superconductivity technology. The potential benefits are multiple comprising weight, dimension and cost reduction in both capital and operating costs. In this paper a rough analytical design is presented of an MgB2 fully superconducting wind turbine generator (WTG). An analytical current sheet distribution is adopted to calculate the magnetic field of the generator and a finite element method (FEM) analysis is used to verify the field calculation. The objective of this work is to assess the technical feasibility of this generator topology and attempt to extract more general conclusions regarding the potential application of superconducting drivetrains in offshore wind turbines.","","en","conference paper","European Wind Energy Association","","","","","","","","Electrical Engineering, Mathematics and Computer Science","Electrical Sustainable Energy","","","","" "uuid:7a2dcf0b-e88e-4da6-baa9-59cfc4cc63ad","http://resolver.tudelft.nl/uuid:7a2dcf0b-e88e-4da6-baa9-59cfc4cc63ad","Robustness and Optimization of Complex Networks: Reconstructability, Algorithms and Modeling","Liu, D.","Van Mieghem, P. (promotor)","2013","The infrastructure networks, including the Internet, telecommunication networks, electrical power grids, transportation networks (road, railway, waterway, and airway networks), gas networks and water networks, are becoming more and more complex. The complex infrastructure networks are crucial to our human society, and it has been a hot research eld to make our complex infrastructure networks more robust and optimize the performance of them. Besides man-designed infrastructure networks, complex networks also cover many natural networks, such as social networks, ecological networks, and biological networks. In order to tackle some of the di¢ cult social issues, ecological problems, and unsolved medical problems, we must learn how these natural complex networks organize, operate, and function. Complex networks can be represented by graphs. A graph consists of a collection of nodes and a collection of links that connect the nodes. A graph is uniquely described by its adjacency matrix, of which the entry on row i and column j is one only if node i and node j in the graph is connected by a link, otherwise the entry is zero. Each adjacency matrix is associated to a unique set of eigenvalues and corresponding eigenvectors. The eigenvalues and corresponding eigenvectors of a graph, also called the spectrum of the graph, contains all the information of the graph, and the topological/physical meanings of some eigenvalues and eigenvectors are already known. The knowledge on the spectra of networks is of crucial importance to the many aspects of the researches on complex network, such as connectivity of networks and virus spreading in networks. The line graph l (G) of a graph G has a set of nodes mapping the set of links in G, and two nodes in l (G) are adjacent if and only if the corresponding links in G have a node in common. Some problems of graphs can be transformed to much easier ones in the domain of line graphs. For example, partitioning the nodes to nd the overlapping communities in a graph can be done by partitioning the links in the line graph of the concerned graph. Moreover, the line graphs often share common features with real-world complex networks, like highly clustered and assortative mixing. Hence, the line graphs are considered by many to model real-world complex networks. The robustness and optimization of complex network is a rather broad research fi eld. We focus on the reconstruction of complex networks from the spectral domain and the line graph domain. This thesis is organized as follows. We first study the reconstruction of networks from their eigenvalues and eigenvectors and the spectral properties of networks. In the second part of this thesis, we present two algorithms which reconstruct networks from the line graph domain, the properties of the line graphs, and a random line graph model. We at last give the research results on two types of real-world networks. The adjacency matrix of a graph can be computed with its eigenvalues and eigenvectors. When some of the eigenvalues are set to zero, the adjacency matrix can still be correctly computed. We propose a measure, the reconstructability coefficient, de fined as the maximum number of eigenvalues that can be removed. We find that the reconstructability coefficient is linear function of the size of the network for all networks that we have studied. We give some results on the spectral metric, the energy of a graph, which is de fined by the sum of the absolute value of all the eigenvalues. We also explore the relations between graph energy and the topological metric, assortativity, for many different types of networks. For the reconstruction of networks from the line graph domain, we propose two algorithms Marinlinga and Iligra. While all previous algorithms rely on Whitney's theorem, Marinlinga is based on the principle of link relabeling and endnode recognition. Iligra reconstructs the graphs from the line graph domain with the linear time complexity. This thesis extends the researches in the line graph domain. We fi nd that the number of links in a line graph with a fi xed number of nodes can not take some consecutive natural numbers, and these numbers are called a bandgap of the line graph. We present the exact expressions of the bands and bandgaps of the number of links in line graphs. In order to facilitate the researches in the line graph domain, we propose a model which randomly generates line graphs. The essence of our model is to merge step by step a pair of nodes in cliques, subjecting to some rules to ensure that the resulting graphs are line graphs. Thanks to the random line model, a method to generate a serial of graphs of which the assortativity increases linearly has been invented. This thesis studies two types of real-world networks: social networks and human brain networks. We characterize the overlapping community structure of the social networks of ArXiv coauthorship, IMDB actors collaboration and SourceForge collaboration, and propose a growing hypergraph model, based on preferential attachment. The proposed hypergraph model captures the fundamental properties including the power-law distributions of group size, group degree, overlapping depth, individual degree and interest-sharing number of real-world affiliation networks, and reproduces the properties of high clustering, assortative mixing and short average path length of social networks. To study brain networks, we propose a spectral randomness metric to quantize the randomness of networks. Based on the randomness measuring method, we have found that the brain networks of Alzheimers disease are statistically more random than the healthy brain networks.","complex networks; graph spectra; reconstructability; line graphs; social networks; community structure; hypergraphs; brain networks; randomness","en","doctoral thesis","Next Generation Infrastructures Foundation","","","","","","","","Electrical Engineering, Mathematics and Computer Science","Intelligent Systems","","","","" "uuid:fb00d912-6de2-401a-abe7-0bb3a90aaf30","http://resolver.tudelft.nl/uuid:fb00d912-6de2-401a-abe7-0bb3a90aaf30","Random line graphs and a linear law for assortativity","Liu, D.; Trajanovski, S.; Van Mieghem, P.","","2013","For a fixed number N of nodes, the number of links L in the line graph H(N,L) can only appear in consecutive intervals, called a band of L. We prove that some consecutive integers can never represent the number of links L in H(N,L), and they are called a bandgap of L. We give the exact expressions of bands and bandgaps of L. We propose a model which can randomly generate simple graphs which are line graphs of other simple graphs. The essence of our model is to merge step by step a pair of nodes in cliques, which we use to construct line graphs. Obeying necessary rules to ensure that the resulting graphs are line graphs, two nodes to be merged are randomly chosen at each step. If the cliques are all of the same size, the assortativity of the line graphs in each step are close to 0, and the assortativity of the corresponding root graphs increases linearly from ?1 to 0 with the steps of the nodal merging process. If we dope the constructing elements of the line graphs—the cliques of the same size—with a relatively smaller number of cliques of different size, the characteristics of the assortativity of the line graphs is completely altered. We also generate line graphs with the cliques whose sizes follow a binomial distribution. The corresponding root graphs, with binomial degree distributions, zero assortativity, and semicircle eigenvalue distributions, are equivalent to Erd?s-Rényi random graphs.","","en","journal article","American Physical Society","","","","","","","","Electrical Engineering, Mathematics and Computer Science","","","","","" "uuid:bf9fac6a-9ca8-499f-b3d5-1d4ce29c90b9","http://resolver.tudelft.nl/uuid:bf9fac6a-9ca8-499f-b3d5-1d4ce29c90b9","Characterizing the Structure of Affiliation Networks","Liu, D.; Blenn, N.; Van Mieghem, P.F.A.","","2012","ur society contains all types of organizations, such as companies, research groups and hobby clubs. Affliation networks, as a large and important portion of social networks, consist of individuals and their affiation relations: Two individuals are connected by a link if they belong to the same organization(s). Affliation networks naturally contain many fully connected cliques, since the nodes of the same organization are all connected with each other by de?nition. In this paper, we present methods which facilitate the computation for characterizing the real-world affliation networks of ArXiv coauthorship, IMDB actors collaboration and SourceForge collaboration. We propose a growing hypergraph model with preferential attachment for affliation networks which reproduces the clique structure of af?liation networks. By comparing computational results of our model with measurements of the real-world affliation networks of ArXiv coauthorship, IMDB actors collaboration and SourceForge collaboration, we show that our model captures the fundamental properties including the power-law distributions of group size, group degree, overlapping depth, individual degree and interest-sharing number of real-world affliation networks, and reproduces the properties of high clustering, assortative mixing and short average path length of real-world affliation networks.","affliation network; hypergraph; line graph; eigvalue; power law","en","journal article","Elsevier","","","","","","","","Electrical Engineering, Mathematics and Computer Science","Intelligent Systems","","","","" "uuid:5878951a-cd72-4c06-8407-0b7c0d187ef3","http://resolver.tudelft.nl/uuid:5878951a-cd72-4c06-8407-0b7c0d187ef3","A Social Network Model Exhibiting Tunable Overlapping Community Structure","Liu, D.; Blenn, N.; Van Mieghem, P.F.A.","","2012","Social networks, as well as many other real-world networks, exhibit overlapping community structure. In this paper, we present formulas which facilitate the computation for characterizing the overlapping community structure of networks. A hypergraph representation of networks with overlapping community structure is introduced. Using the hypergraph representation we setup a social network model which exhibits innate tunable overlapping community structure. By comparing simulation results of our model with results of the Hyves network and the SourceForge network, we show that our model captures most of the common features of large social networks. We analytically give the relation between the maximum membership number of a network and the adjacency eigenvalues of the simple graph representation of the network, which is the line graph of the hypergraph representation.","social networks; overlapping community structure; preferential attachment; hypergraph","en","journal article","Elsevier","","","","","","","","Electrical Engineering, Mathematics and Computer Science","Intelligent Systems","","","","" "uuid:46dedfa7-d6e7-4f29-88f7-a7ea0a8b87d1","http://resolver.tudelft.nl/uuid:46dedfa7-d6e7-4f29-88f7-a7ea0a8b87d1","Decreasing the spectral radius of a graph by link removals","Van Mieghem, P.; Stevanovi?, D.; Kuipers, F.; Li, C.; Van de Bovenkamp, R.; Liu, D.; Wang, H.","","2011","The decrease of the spectral radius, an important characterizer of network dynamics, by removing links is investigated. The minimization of the spectral radius by removing m links is shown to be an NP-complete problem, which suggests considering heuristic strategies. Several greedy strategies are compared, and several bounds on the decrease of the spectral radius are derived. The strategy that removes that link l=i~j with largest product (x1)i(x1)j of the components of the eigenvector x1 belonging to the largest adjacency eigenvalue is shown to be superior to other strategies in most cases. Furthermore, a scaling law where the decrease in spectral radius is inversely proportional to the number of nodes N in the graph is deduced. Another sublinear scaling law of the decrease in spectral radius versus the number m of removed links is conjectured.","","en","journal article","American Physical Society","","","","","","","","Electrical Engineering, Mathematics and Computer Science","Telecommunications","","","","" "uuid:a70dcd65-8114-458d-b61a-5cd8d46f54eb","http://resolver.tudelft.nl/uuid:a70dcd65-8114-458d-b61a-5cd8d46f54eb","Spectral perturbation and reconstructability of complex networks","Liu, D.; Wang, H.; Van Mieghem, P.","","2010","In recent years, many network perturbation techniques, such as topological perturbations and service perturbations, were employed to study and improve the robustness of complex networks. However, there is no general way to evaluate the network robustness. In this paper, we propose a global measure for a network, the reconstructability coefficient ?, defined as the maximum number of eigenvalues that can be removed, subject to the condition that the adjacency matrix can be reconstructed exactly. Our main finding is that a linear scaling law, E[?]=aN, seems universal in that it holds for all networks that we have studied.","","en","journal article","American Physical Society","","","","","","","","Electrical Engineering, Mathematics and Computer Science","Telecommunications","","","",""