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Exact coupling threshold for structural transition reveals diversified behaviors in interconnected networks

Sahneh, F.D. (author), Scoglio, C. (author), Van Mieghem, P. (author)

An interconnected network features a structural transition between two regimes [F. Radicchi and A. Arenas, Nat. Phys. 9, 717 (2013)]: one where the network components are structurally distinguishable and one where the interconnected network functions as a whole. Our exact solution for the coupling threshold uncovers network topologies with...

journal article 2015

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From epidemics to information propagation: Striking differences in structurally similar adaptive network models

Trajanovski, S. (author), Guo, D. (author), Van Mieghem, P.F.A. (author)

The continuous-time adaptive susceptible-infected-susceptible (ASIS) epidemic model and the adaptive information diffusion (AID) model are two adaptive spreading processes on networks, in which a link in the network changes depending on the infectious state of its end nodes, but in opposite ways: (i) In the ASIS model a link is removed between...

journal article 2015

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Survival time of the susceptible-infected-susceptible infection process on a graph

Van de Bovenkamp, R. (author), Van Mieghem, P. (author)

The survival time T is the longest time that a virus, a meme, or a failure can propagate in a network. Using the hitting time of the absorbing state in an uniformized embedded Markov chain of the continuous-time susceptible-infected-susceptible (SIS) Markov process, we derive an exact expression for the average survival time E[T ] of a virus in...

journal article 2015

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Accuracy criterion for the mean-field approximation in susceptible-infected-susceptible epidemics on networks

Van Mieghem, P.F.A. (author), Van de Bovenkamp, R. (author)

Mean-field approximations (MFAs) are frequently used in physics. When a process (such as an epidemic or a synchronization) on a network is approximated by MFA, a major hurdle is the determination of those graphs for which MFA is reasonably accurate. Here, we present an accuracy criterion for Markovian susceptible-infected-susceptible (SIS)...

journal article 2015

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Epidemic outbreaks in two-scale community networks

Bonaccorsi, S. (author), Ottaviano, S. (author), De Pellegrini, F. (author), Socievole, A. (author), Van Mieghem, P.F.A. (author)

We consider a model for the diffusion of epidemics in a population that is partitioned into local communities. In particular, assuming a mean-field approximation, we analyze a continuous-time susceptible-infected-susceptible (SIS) model that has appeared recently in the literature. The probability by which an individual infects individuals in...

journal article 2014

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Nodal infection in Markovian susceptible-infected-susceptible and susceptible-infected-removed epidemics on networks are non-negatively correlated

Cator, E. (author), Van Mieghem, P.F.A. (author)

By invoking the famous Fortuin, Kasteleyn, and Ginibre (FKG) inequality, we prove the conjecture that the correlation of infection at the same time between any pair of nodes in a network cannot be negative for (exact) Markovian susceptible-infected-susceptible (SIS) and susceptible-infected-removed (SIR) epidemics on networks. The truth of the...

journal article 2014

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Domination-time dynamics in susceptible-infected-susceptible virus competition on networks

Van de Bovenkamp, R. (author), Kuipers, F.A. (author), Van Mieghem, P.F.A. (author)

When two viruses compete for healthy nodes in a simple network and both spreading rates are above the epidemic threshold, only one virus will survive. However, if we prevent the viruses from dying out, rich dynamics emerge. When both viruses are identical, one virus always dominates the other, but the dominating and dominated virus alternate. We...

journal article 2014

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Epidemic threshold in directed networks

Li, C. (author), Wang, H. (author), Van Mieghem, P.F.A. (author)

Epidemics have so far been mostly studied in undirected networks. However, many real-world networks, such as the online social network Twitter and the world wide web, on which information, emotion, or malware spreads, are directed networks, composed of both unidirectional links and bidirectional links. We define the directionality ? as the...

journal article 2013

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Epidemic threshold and topological structure of susceptible-infectious-susceptible epidemics in adaptive networks

Guo, D. (author), Trajanovski, S. (author), Van de Bovenkamp, R. (author), Wang, H. (author), Van Mieghem, P.F.A. (author)

The interplay between disease dynamics on a network and the dynamics of the structure of that network characterizes many real-world systems of contacts. A continuous-time adaptive susceptible-infectious-susceptible (ASIS) model is introduced in order to investigate this interaction, where a susceptible node avoids infections by breaking its...

journal article 2013

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Effect of the interconnected network structure on the epidemic threshold

Wang, H. (author), Li, Q. (author), D'Agostino, G. (author), Havlin, S. (author), Stanley, H.E. (author), Van Mieghem, P. (author)

Most real-world networks are not isolated. In order to function fully, they are interconnected with other networks, and this interconnection influences their dynamic processes. For example, when the spread of a disease involves two species, the dynamics of the spread within each species (the contact network) differs from that of the spread...

journal article 2013

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Susceptible-infected-susceptible epidemics on networks with general infection and cure times

Cator, E. (author), Van de Bovenkamp, R. (author), Van Mieghem, P.F.A. (author)

The classical, continuous-time susceptible-infected-susceptible (SIS) Markov epidemic model on an arbitrary network is extended to incorporate infection and curing or recovery times each characterized by a general distribution (rather than an exponential distribution as in Markov processes). This extension, called the generalized SIS (GSIS)...

journal article 2013

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Non-Markovian Infection Spread Dramatically Alters the Susceptible-Infected-Susceptible Epidemic Threshold in Networks

Van Mieghem, P.F.A. (author), Van de Bovenkamp, R. (author)

Most studies on susceptible-infected-susceptible epidemics in networks implicitly assume Markovian behavior: the time to infect a direct neighbor is exponentially distributed. Much effort so far has been devoted to characterize and precisely compute the epidemic threshold in susceptible-infected-susceptible Markovian epidemics on networks. Here,...

journal article 2013

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Random line graphs and a linear law for assortativity

Liu, D. (author), Trajanovski, S. (author), Van Mieghem, P. (author)

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...

journal article 2013

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Susceptible-infected-susceptible epidemics on the complete graph and the star graph: Exact analysis

Cator, E.A. (author), Van Mieghem, P. (author)

Since mean-field approximations for susceptible-infected-susceptible (SIS) epidemics do not always predict the correct scaling of the epidemic threshold of the SIS metastable regime, we propose two novel approaches: (a) an ?-SIS generalized model and (b) a modified SIS model that prevents the epidemic from dying out (i.e., without the...

journal article 2013

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Susceptible-infected-susceptible model: A comparison of N-intertwined and heterogeneous mean-field approximations

Li, C. (author), Van de Bovenkamp, R. (author), Van Mieghem, P.F.A. (author)

We introduce the ?-susceptible-infected-susceptible (SIS) spreading model, which is taken as a benchmark for the comparison between the N-intertwined approximation and the Pastor-Satorras and Vespignani heterogeneous mean-field (HMF) approximation of the SIS model. The N-intertwined approximation, the HMF approximation, and the ?-SIS spreading...

journal article 2012

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Epidemics in networks with nodal self-infection and the epidemic threshold

Van Mieghem, P.F.A. (author), Cator, E. (author)

Since the Susceptible-Infected-Susceptible (SIS) epidemic threshold is not precisely defined in spite of its practical importance, the classical SIS epidemic process has been generalized to the ??SIS model, where a node possesses a self-infection rate ?, in addition to a link infection rate ? and a curing rate ?. The exact Markov equations are...

journal article 2012

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Second-order mean-field susceptible-infected-susceptible epidemic threshold

Cator, E. (author), Van Mieghem, P. (author)

conference paper 2012

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Decreasing the spectral radius of a graph by link removals

Van Mieghem, P. (author), Stevanovi?, D. (author), Kuipers, F. (author), Li, C. (author), Van de Bovenkamp, R. (author), Liu, D. (author), Wang, H. (author)

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...

journal article 2011

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Spectral graph analysis of modularity and assortativity

Van Mieghem, P.F.A. (author), Ge, X. (author), Schumm, P. (author), Trajanovski, S. (author), Wang, H. (author)

Expressions and bounds for Newman’s modularity are presented. These results reveal conditions for or properties of the maximum modularity of a network. The influence of the spectrum of the modularity matrix on the maximum modularity is discussed. The second part of the paper investigates how the maximum modularity, the number of clusters, and...

journal article 2010

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Effect of tumor resection on the characteristics of functional brain networks

Wang, H. (author), Douw, L. (author), Hernández, J.M. (author), Reijneveld, J.C. (author), Stam, C.J. (author), Van Mieghem, P. (author)

Brain functioning such as cognitive performance depends on the functional interactions between brain areas, namely, the functional brain networks. The functional brain networks of a group of patients with brain tumors are measured before and after tumor resection. In this work, we perform a weighted network analysis to understand the effect of...

journal article 2010