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Asymmetric Relations and the Friendship Paradox

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Document pages: 20 pages

Abstract: The friendship paradox says that your friends have more friends than you. The result assumes symmetric relations: if two people are friends, then each is the other s friend. For social networks that satisfy this assumption (e.g., Facebook), the friendship paradox implies that firms can potentially achieve faster and more widespread diffusion of information by seeding it with the friends of a group of people than with people in the group itself. We generalize the result to allow one-sided (leader follower) relations and examine the implications for seeding in social networks where messages can be sent only by a leader to his her followers. We obtain necessary and sufficient conditions under which the highest number of followers is obtained by seeding with (1) leaders, (2) followers, and (3) individuals chosen by ignoring the distinction between leaders and followers. We examine the seeding implications of the results for a subset of Twitter users.

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