# Piet Van Mieghem's research while affiliated with Delft University of Technology and other places

## Publications (359)

Preprint
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We propose a linear clustering process on a network consisting of two opposite forces: attraction and repulsion between adjacent nodes. Each node is mapped to a position on a one-dimensional line. The attraction and repulsion forces move the nodal position on the line, depending on how similar or different the neighbourhoods of two adjacent nodes a...
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The $k$-th power of the adjacency matrix of a simple undirected graph represents the number of walks with length $k$ between pairs of nodes. As a walk where no node repeats, a path is a walk where each node is only visited once. The set of paths constitutes a relatively small subset of all possible walks. We introduce three types of walks, represen...
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Epilepsy surgery is the treatment of choice for drug-resistant epilepsy patients, but one in three patients continue to have seizures one year after surgery. In order to improve the chances of good outcomes, computational models of seizure dynamics are being integrated into surgical planning to simulate the effects of the planned surgeries. These m...
Article
In this paper, we focus on the link density in random geometric graphs (RGGs) with a distance-based connection function. After deriving the link density in D dimensions, we focus on the two-dimensional (2D) and three-dimensional (3D) space and show that the link density is accurately approximated by the Fréchet distribution, for any rectangular spa...
Article
The influence of people's individual responses to the spread of contagious phenomena, like the COVID-19 pandemic, is still not well understood. We investigate the Markovian Generalized Adaptive Susceptible-Infected-Susceptible (G-ASIS) epidemic model. The G-ASIS model comprises many contagious phenomena on networks, ranging from epidemics and infor...
Article
The imposition of lockdowns in response to the COVID-19 outbreak has underscored the importance of human behavior in mitigating virus transmission. The scientific study of interventions designed to change behavior (e.g., to promote physical distancing) requires measures of effectiveness that are fast, that can be assessed through experiments, and t...
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How temporal modulations in functional interactions are shaped by the underlying anatomical connections remains an open question. Here, we analyse the role of structural eigenmodes, in the formation and dissolution of temporally evolving functional brain networks using resting‐state magnetoencephalography and diffusion magnetic resonance imaging da...
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Epilepsy surgery is the treatment of choice for drug-resistant epilepsy patients. However, seizure-freedom is currently achieved in only 2/3 of the patients after surgery. In this study we have developed an individualized computational model based on MEG brain networks to explore seizure propagation and the efficacy of different virtual resections....
Article
During the outbreak of a virus, perhaps the greatest concern is the future evolution of the epidemic: How many people will be infected and which regions will be affected the most? The accurate prediction of an epidemic enables targeted disease countermeasures (e.g., allocating medical staff and quarantining). But when can we trust the prediction of...
Chapter
We introduce a Markov Modulated Process (MMP) to describe human mobility. We represent the mobility process as a time-varying graph, where a link specifies a connection between two nodes (humans) at any discrete time step. Each state of the Markov chain encodes a certain modification to the original graph. We show that our MMP model successfully ca...
Chapter
Despite many studies on the transmission mechanism of the Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), it remains still challenging to efficiently reduce mortality. In this work, we apply a two-population Susceptible-Infected-Removed (SIR) model to investigate the COVID-19 spreading when contacts between elderly and non-elderly ind...
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The success of epilepsy surgery in patients with refractory epilepsy depends upon correct identification of the epileptogenic zone (EZ) and an optimal choice of the resection area. In this study we developed individualized computational models based upon structural brain networks to explore the impact of different virtual resections on the propagat...
Preprint
Full-text available
Background Epilepsy surgery is the treatment of choice for drug-resistant epilepsy patients. However, seizure-freedom is currently achieved in only 2/3 of the patients after surgery. In this study we have developed an individualized computational model based on functional brain networks to explore seizure propagation and the efficacy of different v...
Preprint
Despite many studies on the transmission mechanism of the Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), it remains still challenging to efficiently reduce mortality. In this work, we apply a two-population Susceptible-Infected-Removed (SIR) model to investigate the COVID-19 spreading when contacts between elderly and non-elderly ind...
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Large-scale neurophysiological networks are often reconstructed from band-pass filtered time series derived from magnetoencephalography (MEG) data. Common practice is to reconstruct these networks separately for different frequency bands and to treat them independently. Recent evidence suggests that this separation may be inadequate, as there can b...
Article
Infectious diseases typically spread over a contact network with millions of individuals, whose sheer size is a tremendous challenge to analyzing and controlling an epidemic outbreak. For some contact networks, it is possible to group individuals into clusters. A high-level description of the epidemic between a few clusters is considerably simpler...
Article
In this paper, we propose closed-form analytic approximations for the number of controllable nodes in sparse communication networks from the aspect of network controllability, considering link-based random attack, targeted attack, as well as random attack under the protection of critical links. We compare our approximations with simulation results...
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Optical networks are vulnerable to failures due to targeted attacks or large-scale disasters. The recoverability of optical networks refers to the ability of an optical network to return to a desired performance level after suffering topological perturbations such as link failures. This paper proposes a general topological approach and recoverabili...
Preprint
Full-text available
Background The success of epilepsy surgery in patients with refractory epilepsy depends upon correct identification of the epileptogenic zone (EZ) and an optimal choice of the resection area. In this study we developed individualized computational models based upon structural brain networks to explore the impact of different virtual resections on t...
Article
Many clustering algorithms for complex networks depend on the choice for the number of clusters and it is often unclear how to make this choice. The number of eigenvalues located outside a circle in the spectrum of the non-backtracking matrix was conjectured to be an estimator of the number of clusters in a graph. We compare the estimate of the num...
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Multimodal freight transport allows switching among different modes of transport to utilize transport facilities more efficiently. This paper proposes an approach on network modeling and robustness assessment for multimodal freight transport networks, where the nodes represent junctions, terminals and crossings, and the links represent pathways. Th...
Preprint
Full-text available
Infectious diseases typically spread over a contact network with millions of individuals, whose sheer size is a tremendous challenge to analysing and controlling an epidemic outbreak. For some contact networks, it is possible to group individuals into clusters. A high-level description of the epidemic between a few clusters is considerably simpler...
Preprint
We investigate Binet's \emph{convergent} series for the logarithm of the Gamma function and contribute to the classical theory of the Gamma function by correcting an unfortunate error in Binet's original computation. We compare the corrected Binet series with Stirling's \emph{asymptotic} expansion and discuss the advantage of both series.
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The majority of epidemic models are described by non-linear differential equations which do not have a closed-form solution. Due to the absence of a closed-form solution, the understanding of the precise dynamics of a virus is rather limited. We solve the differential equations of the N-intertwined mean-field approximation of the susceptible-infect...
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Initially emerged in the Chinese city Wuhan and subsequently spread almost worldwide causing a pandemic, the SARS-CoV-2 virus follows reasonably well the Susceptible–Infectious–Recovered (SIR) epidemic model on contact networks in the Chinese case. In this paper, we investigate the prediction accuracy of the SIR model on networks also for Italy. Sp...
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Initially emerged in the Chinese city Wuhan and subsequently spread almost worldwide causing a pandemic, the SARS-CoV-2 virus follows reasonably well the SIR (Susceptible-Infectious-Recovered) epidemic model on contact networks in the Chinese case. In this paper, we investigate the prediction accuracy of the SIR model on networks also for Italy. Sp...
Article
This article studies the dynamics of complex networks with a time-invariant underlying topology, composed of nodes with linear internal dynamics and linear dynamic interactions between them. While graph theory defines the underlying topology of a network, a linear time-invariant state-space model analytically describes the internal dynamics of each...
Preprint
Several exact expansions as well as lower and upperbounds of the Kermack and McKendrick SIR equations are presented.
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Researchers from various scientific disciplines have attempted to forecast the spread of coronavirus disease 2019 (COVID-19). The proposed epidemic prediction methods range from basic curve fitting methods and traffic interaction models to machine-learning approaches. If we combine all these approaches, we obtain the Network Inference-based Predict...
Chapter
The failures of multiple elements in a network can have disastrous consequences on its operation. Therefore, understanding the robustness of networks that experience multiple failures is utterly important. In this chapter, we review well-defined metrics related to the topology and resilience of the network and use them to analyze the robustness of...
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Abstract At the moment of writing, the future evolution of the COVID-19 epidemic is unclear. Predictions of the further course of the epidemic are decisive to deploy targeted disease control measures. We consider a network-based model to describe the COVID-19 epidemic in the Hubei province. The network is composed of the cities in Hubei and their i...
Preprint
Currently, many countries are considering the introduction of tracing software on mobile smartphones with the main purpose to inform and alarm the mobile app user. Here, we demonstrate that, in addition to alarming and informing, mobile tracing can detect nearly all individuals that are infected by SARS-CoV-2, including the notorious asymptomatic i...
Preprint
The imposition of lockdowns in response to the COVID-19 outbreak has underscored the importance of human behavior in mitigating virus transmission. Scientific study ofinterventions designed to change behavior (e.g., to promote social distancing) requiresmeasures of effectiveness that are fast, that can be assessed through experiments, and that can...
Preprint
Processes on networks consist of two interdependent parts: the network topology, consisting of the links between nodes, and the dynamics, specified by some governing equations. This work considers the prediction of the future dynamics on an unknown network, based on past observations of the dynamics. For a general class of governing equations, we p...
Preprint
We review the function theoretical properties of the Mittag-Leffler function $E_{a,b}\left( z\right)$ in a self-contained manner, but also add new results.
Article
The average fraction of infected nodes, in short the prevalence, of the Markovian ɛ-SIS (susceptible-infected-susceptible) process with small self-infection rate ɛ>0 exhibits, as a function of time, a typical “two-plateau” behavior, which was first discovered in the complete graph KN. Although the complete graph is often dismissed as an unacceptabl...
Article
In the classical susceptible-infected-susceptible (SIS) model, a disease or infection spreads over a given, mostly fixed graph. However, in many real complex networks, the topology of the underlying graph can change due to the influence of the dynamical process. In this paper, besides the spreading process, the network adaptively changes its topolo...
Article
The underlying core of most epidemic models is the graph that specifies the contacts between healthy and infected individuals. However, in the majority of applications, the contact network is unknown. To understand and predict an epidemic outbreak nonetheless, network reconstruction methods aim to estimate the contact network from viral state obser...
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Functional brain networks are shaped and constrained by the underlying structural network. However, functional networks are not merely a one-to-one reflection of the structural network. Several theories have been put forward to understand the relationship between structural and functional networks. However, it remains unclear how these theories can...
Article
The ɛ–susceptible-infected-susceptible (SIS) epidemic model on a graph adds an independent, Poisson self-infection process with rate ɛ to the “classical” Markovian SIS process. The steady state in the classical SIS process (with ɛ=0) on any finite graph is the absorbing or overall-healthy state, in which the virus is eradicated from the network. We...
Preprint
At the moment of writing (11 February, 2020), the future evolution of the 2019-nCoV virus is unclear. Predictions of the further course of the epidemic are decisive to deploy targeted disease control measures. We consider a network-based model to describe the 2019-nCoV epidemic in the Hubei province. The network is composed of the cities in Hubei a...
Article
We study the electrodynamic impedance of percolating conductors with a predefined network topology using a scanning microwave impedance microscope at gigahertz frequencies. For a given percolation number we observe strong spatial variations across a sample that correlate with the connected regions (clusters) in the network when the resistivity is l...
Chapter
Existing link attack strategies in networks differ in the importance or robustness metric, that quantifies the effect of a link removal upon the network’s vulnerability. In this paper, we investigate the role of the effective resistance matrix in the removal of links on a graph and compare this removal strategy with other state-of-the-art attack st...
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Dynamical processes running on different networks behave differently, which makes the reconstruction of the underlying network from dynamical observations possible. However, to what level of detail the network properties can be determined from incomplete measurements of the dynamical process is still an open question. In this paper, we focus on the...
Chapter
We have so far concentrated on networks, which do not change over time. In reality, a network may change over time in an independent process from the epidemic spread. Such networks, where the topology changes according to some rule or pattern, are known as evolving networks. The epidemic threshold in evolving networks has been studied in the past [...
Chapter
A community structure is an important non-trivial topological feature of a complex networks. Indeed community structures are a typical feature of social networks, tightly connected groups of nodes in the World Wide Web usually correspond to pages on common topics, communities in cellular and genetic networks are related to functional modules [46].
Article
The N-Intertwined Mean Field Approximation (NIMFA) is a reasonably accurate approximation of the exact SIS epidemic process on a network. The average fraction of infected nodes in the NIMFA steady state, also called the steady-state prevalence, in terms of the effective infection rate can be expanded into a power series around the NIMFA epidemic th...
Preprint
The symmetric nonnegative inverse eigenvalue problem (SNIEP) asks which sets of numbers (counting multiplicities) can be the eigenvalues of a symmetric matrix with nonnegative entries. While examples of such matrices are abundant in linear algebra and various applications, this question is still open for matrices of dimension $N\geq 5$. One of the...
Preprint
Full-text available
We study the electrodynamic impedance of percolating conductors with a pre-defined network topology using a scanning microwave impedance microscope (sMIM) at GHz frequencies. For a given percolation number we observe strong spatial variations across a sample which correlate with the connected regions (clusters) in the network when the resistivity i...
Preprint
Full-text available
We study the electrodynamic impedance of percolating conductors with a pre-defined network topology using a scanning microwave impedance microscope (sMIM) at GHz frequencies. For a given percolation number we observe strong spatial variations across a sample which correlate with the connected regions (clusters) in the network when the resistivity i...
Preprint
Full-text available
Although non-Markovian processes are considerably more complicated to analyse, real-world epidemics are likely non-Markovian, because the infection time is not always exponentially distributed. Here, we present analytic expressions of the epidemic threshold in a Weibull and a Gamma SIS epidemic on any network, where the infection time is Weibull, r...
Article
Graphs are a central object of study in various scientific fields, such as discrete mathematics, theoretical computer science and network science. These graphs are typically studied using combinatorial, algebraic or probabilistic methods, each of which highlights the properties of graphs in a unique way. Here, we discuss a novel approach to study g...
Article
Full-text available
Clinical network neuroscience, the study of brain network topology in neurological and psychiatric diseases, has become a mainstay field within clinical neuroscience. Being a multidisciplinary group of clinical network neuroscience experts based in The Netherlands, we often discuss the current state of the art and possible avenues for future invest...
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In networked spreading models, each node can infect its neighbors and cure spontaneously. The curing is assumed to occur uniformly over time. A pulse immunization/curing strategy is more efficient and broadly applied to suppressing spreading processes. We model the epidemic process by the basic Susceptible-Infected (SI) process with a pulse curing...
Preprint
The majority of research on epidemics relies on models which are formulated in continuous-time. However, real-world epidemic data is gathered and processed in a digital manner, which is more accurately described by discrete-time epidemic models. We analyse the discrete-time NIMFA epidemic model on directed networks with heterogeneous spreading para...
Article
The cut-set ∂V in a graph is defined as the set of all links between a set of nodes V and all other nodes in that graph. Finding bounds for the size of a cut-set |∂V| is an important problem, and is related to mixing times, connectedness and spreading processes on networks. A standard way to bound the number of links in a cut-set |∂V| relies on Lap...
Article
Networks are often made up of several layers that exhibit diverse degrees of interdependencies. An interdependent network consists of a set of graphs G that are interconnected through a weighted interconnection matrix B, where the weight of each intergraph link is a non-negative real number p. Various dynamical processes, such as synchronization, c...
Chapter
Direct connections between nodes usually result in efficient transmission in networks. Such electric power transmission is governed by physical laws, and an assessment purely based on direct connections between nodes and shortest paths may not capture the operation of power grids. Motivated by these facts, in this chapter, we investigate the relati...
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To shed light on the disease localization phenomenon, we study a bursty susceptible-infected-susceptible (SIS) model and analyze the model under the mean-field approximation. In the bursty SIS model, the infected nodes infect all their neighbors periodically, and the near-threshold steady-state prevalence is non-constant and maximized by a factor e...
Article
Induced spreading aims to maximize the infection probabilities of some target nodes by adjusting the nodal infection rates, which can be applied in biochemical and information spreading. We assume that the adjustment of the nodal infection rates has an associated cost and formulate the induced spreading for SIS epidemics in networks as an optimizat...
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Predicting the viral dynamics of an epidemic process requires the knowledge of the underlying contact network. However, the network is not known for most applications and has to be inferred from observing the viral state evolution instead. We propose a polynomial-time network reconstruction algorithm for the discrete-time NIMFA model based on a bas...
Preprint
Full-text available
To shed light on the disease localization phenomenon, we study a bursty susceptible-infected-susceptible (SIS) model and analyze the model under the mean-field approximation. In the bursty SIS model, the infected nodes infect all their neighbors periodically, and the near-threshold steady-state prevalence is non-constant and maximized by a factor e...
Article
The SIS dynamics of the spread of a virus crucially depend on both the network topology and the spread parameters. Since neither the topology nor the spread parameters are known for the majority of applications, they have to be inferred from observations of the virus spread. We propose an inference method for both topology and spread parameters bas...
Article
Full-text available
Due to the open data policies, nowadays, some countries have their power grid data available online. This may bring a new concern to the power grid operators in terms of malicious threats. In this paper, we assess the vulnerability of power grids to targeted attacks based on network science. By employing two graph models for power grids as simple a...
Article
We emphasize that correlations between infection states in both the SIS and SIR model are always positive and that the title of the article “Nodal infection in Markovian susceptible-infected-susceptible and susceptible-infected-removed epidemics on networks are non-negatively correlated” [Phys. Rev. E 89, 052802 (2014)] is correct. The history and...
Preprint
Networks are often made up of several layers that exhibit diverse degrees of interdependencies. A multilayer interdependent network consists of a set of graphs $G$ that are interconnected through a weighted interconnection matrix $B$, where the weight of each inter-graph link is a non-negative real number $p$. Various dynamical processes, such...
Preprint
Full-text available
The knowledge of the network topology is imperative to precisely describing the viral dynamics of an SIS epidemic process. In scenarios for which the network topology is unknown, one resorts to reconstructing the network from observing the viral state trace. This work focusses on the impact of the viral state observations on the computational compl...
Preprint
Graphs are a central object of study in various scientific fields, such as discrete mathematics, theoretical computer science and network science. These graphs are typically studied using combinatorial, algebraic or probabilistic methods, each of which highlights the properties of graphs in a unique way. Here, we discuss a novel approach to study g...
Preprint
Full-text available
In this paper, we focus on the autocorrelation of the Susceptible-Infected-Susceptible (SIS) process on networks. The N-Intertwined Mean-Field Approximation (NIMFA) is applied to calculate the autocorrelation properties of the exact SIS process. We derive the autocorrelation of the infection state of each node and the fraction of infected nodes bot...
Article
Identifying the fastest spreaders in epidemics on a network helps to ensure an efficient spreading. By ranking the average spreading time for different spreaders, we show that the fastest spreader may change with the effective infection rate of a SIS epidemic process, which means that the time-dependent influence of a node is usually strongly coupl...
Article
In this paper, we study cascading failures in power grids under the nonlinear AC and linearized DC power flow models. We numerically compare the evolution of cascades after single line failures under the two flow models in four test networks. The cascade simulations demonstrate that the assumptions underlying the DC model (e.g., ignoring power loss...
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Since a real epidemic process is not necessarily Markovian, the epidemic threshold obtained under the Markovian assumption may be not realistic. To understand general non-Markovian epidemic processes on networks, we study the Weibullian SIS process in which the infection process is a renewal process with a Weibull time distribution. We find that, i...
Article
There is an increasing awareness of the advantages of multi-modal neuroimaging. Networks obtained from different modalities are usually treated in isolation, which is however contradictory to accumulating evidence that these networks show non-trivial interdependencies. Even networks obtained from a single modality, such as frequency-band specific f...
Article
In a Susceptible–Infected–Susceptible (SIS) process, we investigate the spreading time Tm, which is the time when the number of infected nodes in the metastable state is first reached, starting from the outbreak of the epidemics. We observe that the spreading time Tm resembles a lognormal-like distribution, though with different deep tails, both fo...
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The prevalence, which is the average fraction of infected nodes, has been studied to evaluate the robustness of a network subject to the spread of epidemics. We explore the vulnerability (infection probability) of each node in the metastable state with a given effective infection rate τ. Specifically, we investigate the ranking of the nodal vulnera...