Topics in matrix analysis
Competitive exclusion in gonorrhea models and other sexually transmitted diseases
SIAM Journal on Applied Mathematics
Competitive exclusion and coexistence of multiple strains in an SIS STD model
SIAM Journal on Applied Mathematics
The Mathematics of Infectious Diseases
SIAM Review
Mining knowledge-sharing sites for viral marketing
Proceedings of the eighth ACM SIGKDD international conference on Knowledge discovery and data mining
On the bursty evolution of blogspace
WWW '03 Proceedings of the 12th international conference on World Wide Web
Measuring and Modeling Computer Virus Prevalence
SP '93 Proceedings of the 1993 IEEE Symposium on Security and Privacy
Maximizing the spread of influence through a social network
Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
Information diffusion through blogspace
Proceedings of the 13th international conference on World Wide Web
The dynamics of viral marketing
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Epidemic thresholds in real networks
ACM Transactions on Information and System Security (TISSEC)
Word of Mouth: Rumor Dissemination in Social Networks
SIROCCO '08 Proceedings of the 15th international colloquium on Structural Information and Communication Complexity
Competitive influence maximization in social networks
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
A Generalized Linear Threshold Model for Multiple Cascades
ICDM '10 Proceedings of the 2010 IEEE International Conference on Data Mining
Threshold Conditions for Arbitrary Cascade Models on Arbitrary Networks
ICDM '11 Proceedings of the 2011 IEEE 11th International Conference on Data Mining
Propagation and immunization in large networks
XRDS: Crossroads, The ACM Magazine for Students - Big Data
Rise and fall patterns of information diffusion: model and implications
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Interacting viruses in networks: can both survive?
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Understanding and managing cascades on large graphs
Proceedings of the VLDB Endowment
Competing memes propagation on networks: a case study of composite networks
ACM SIGCOMM Computer Communication Review
Structure and dynamics of information pathways in online media
Proceedings of the sixth ACM international conference on Web search and data mining
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Given two competing products (or memes, or viruses etc.) spreading over a given network, can we predict what will happen at the end, that is, which product will 'win', in terms of highest market share? One may naively expect that the better product (stronger virus) will just have a larger footprint, proportional to the quality ratio of the products (or strength ratio of the viruses). However, we prove the surprising result that, under realistic conditions, for any graph topology, the stronger virus completely wipes-out the weaker one, thus not merely 'winning' but 'taking it all'. In addition to the proofs, we also demonstrate our result with simulations over diverse, real graph topologies, including the social-contact graph of the city of Portland OR (about 31 million edges and 1 million nodes) and internet AS router graphs. Finally, we also provide real data about competing products from Google-Insights, like Facebook-Myspace, and we show again that they agree with our analysis.