The problem of diffusion control on networks has been extensively studied, with applications ranging from marketing to cybersecurity . However, in many applications, such as targeted vulnerability assessment or clinical therapies, one aspires to affect a targeted subset of a network, while limiting the impact on the rest  . We present a novel model in which the principal aim is to optimize graph structure to affect such targeted diffusion. We present an algorithmic approach for solving this problem at scale, using a gradient-based approach that leverages Rayleigh quotients and pseudospectrum theory. In addition, we present a condition for certifying  a targeted subgraph as immune to targeted diffusion . Finally, we demonstrate the effectiveness of our approach through extensive experiments on real and synthetic networks.
The problem of diffusion control on networks has been extensively studied, with applications ranging from marketing to controlling infectious disease . However, in many applications, such as cybersecurity, an attacker may want to attack a targeted subgraph of a network, while limiting the impact on the rest of the network in order to remain undetected . We present a model POTION in which the principal aim is to optimize graph structure to achieve such targeted attacks. We propose an algorithm POTION-ALG for solving the model at scale, using a gradient-based approach that leverages Rayleigh quotients and pseudospectrum theory. In addition, we present a condition for certifying that a targeted subgraph is immune to such attacks . Finally, we demonstrate the effectiveness of our approach through experiments on real and synthetic networks.
R
cybersecurity
controlling infectious disease
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targeted vulnerability assessment or clinical therapies, one aspires to affect a targeted subset
cybersecurity, an attacker may want to attack a targeted subgraph
A
of the network in order to remain undetected
R
novel model
model POTION
R
affect such targeted diffusion. We present an algorithmic approach for solving this problem
achieve such targeted attacks. We propose an algorithm POTION-ALG for solving the model
A
that
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as immune to targeted diffusion
is immune to such attacks
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extensive