document: Winner takes all : competing viruses or ideas on fair-play networks 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 .
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