POTION : Optimizing Graph Structure for Targeted Diffusion

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.

[1]  Jianbo Shi,et al.  Learning Segmentation by Random Walks , 2000, NIPS.

[2]  Alexander Grey,et al.  The Mathematical Theory of Infectious Diseases and Its Applications , 1977 .

[3]  D. Stevanović,et al.  Decreasing the spectral radius of a graph by link removals. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Yang Yang,et al.  Small vulnerable sets determine large network cascades in power grids , 2017, Science.

[5]  Christos Faloutsos,et al.  Patterns of Cascading Behavior in Large Blog Graphs , 2007, SDM.

[6]  Michael Unser,et al.  Hessian Schatten-Norm Regularization for Linear Inverse Problems , 2012, IEEE Transactions on Image Processing.

[7]  Christos Faloutsos,et al.  Node Immunization on Large Graphs: Theory and Algorithms , 2016, IEEE Transactions on Knowledge and Data Engineering.

[8]  Zhihui Wang,et al.  Dynamic Targeting in Cancer Treatment , 2019, Front. Physiol..

[9]  Ambuj K. Singh,et al.  Fighting Opinion Control in Social Networks via Link Recommendation , 2019, KDD.

[10]  Inducing Equilibria in Networked Public Goods Games through Network Structure Modification , 2020, AAMAS.

[11]  Yevgeniy Vorobeychik,et al.  Removing Malicious Nodes from Networks , 2018, AAMAS.

[12]  Hanghang Tong,et al.  MET: A Fast Algorithm for Minimizing Propagation in Large Graphs with Small Eigen-Gaps , 2015, SDM.

[13]  Hanghang Tong,et al.  Node Immunization with Non-backtracking Eigenvalues , 2020, ArXiv.

[14]  Christos Faloutsos,et al.  On the Vulnerability of Large Graphs , 2010, 2010 IEEE International Conference on Data Mining.

[15]  L. Trefethen,et al.  Spectra and pseudospectra : the behavior of nonnormal matrices and operators , 2005 .

[16]  Tamara G. Kolda,et al.  Community structure and scale-free collections of Erdös-Rényi graphs , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Christos Faloutsos,et al.  Graph evolution: Densification and shrinking diameters , 2006, TKDD.

[18]  Christos Faloutsos,et al.  Epidemic thresholds in real networks , 2008, TSEC.

[19]  Éva Tardos,et al.  Maximizing the Spread of Influence through a Social Network , 2015, Theory Comput..

[20]  Chinwendu Enyioha,et al.  Optimal vaccine allocation to control epidemic outbreaks in arbitrary networks , 2013, 52nd IEEE Conference on Decision and Control.

[21]  Cedric E. Ginestet,et al.  Cognitive relevance of the community structure of the human brain functional coactivation network , 2013, Proceedings of the National Academy of Sciences.

[22]  Luca Antiga,et al.  Automatic differentiation in PyTorch , 2017 .

[23]  Jon Kleinberg,et al.  Maximizing the spread of influence through a social network , 2003, KDD '03.

[24]  Ernesto Estrada,et al.  ‘Hubs-repelling’ Laplacian and related diffusion on graphs/networks , 2020 .

[25]  Yevgeniy Vorobeychik,et al.  Data-driven agent-based modeling, with application to rooftop solar adoption , 2015, Autonomous Agents and Multi-Agent Systems.

[26]  Michalis Faloutsos,et al.  Threshold conditions for arbitrary cascade models on arbitrary networks , 2011, 2011 IEEE 11th International Conference on Data Mining.

[27]  Mykel J. Kochenderfer,et al.  Control of epidemics on graphs , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[28]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[29]  Adilson E Motter,et al.  Cascade-based attacks on complex networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  Talal Rahwan,et al.  Attacking Similarity-Based Link Prediction in Social Networks , 2018, AAMAS.

[31]  Piet Van Mieghem,et al.  Epidemic processes in complex networks , 2014, ArXiv.

[32]  Jure Leskovec,et al.  Meme-tracking and the dynamics of the news cycle , 2009, KDD.

[33]  Yoshihiko Hasegawa,et al.  Diffusion-dynamics laws in stochastic reaction networks. , 2018, Physical review. E.

[34]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[35]  José J. Ramasco,et al.  Systemic delay propagation in the US airport network , 2013, Scientific Reports.

[36]  P. Van Mieghem,et al.  Virus Spread in Networks , 2009, IEEE/ACM Transactions on Networking.

[37]  Sudip Saha,et al.  Approximation Algorithms for Reducing the Spectral Radius to Control Epidemic Spread , 2015, SDM.

[38]  Konstantin Avrachenkov,et al.  The Effect of New Links on Google Pagerank , 2006 .

[39]  Wei Chen,et al.  Efficient influence maximization in social networks , 2009, KDD.

[40]  Michalis Faloutsos,et al.  Gelling, and melting, large graphs by edge manipulation , 2012, CIKM.