Evangelism in social networks: Algorithms and complexity

• Published in: Networks Vol. 71; no. 4; pp. 346 - 357
• Main Authors: Cordasco, Gennaro, Gargano, Luisa, Rescigno, Adele Anna, Vaccaro, Ugo
• Format: Journal Article
• Language: English
• Published: New York Wiley Subscription Services, Inc 01-06-2018
• Subjects: Algorithms; Graphs; influence maximization; Information dissemination; Marketing; parametrized complexity; social network; Social networks; spread of influence; Time dependence; viral marketing
• ISSN: 0028-3045; 1097-0037
• DOI: 10.1002/net.21756

We consider a population of interconnected individuals that, with respect to a piece of information, at each time instant can be subdivided into three (time‐dependent) categories: agnostics, influenced, and evangelists. A dynamical process of information diffusion evolves among the individuals of the population according to the following rules. Initially, all individuals are agnostic. Then, a set of people is chosen from the outside and convinced to start evangelizing, that is, to start spreading the information. When a number of evangelists, greater than a given threshold, communicate with a node v, the node v becomes influenced, whereas, as soon as the individual v is contacted by a sufficiently much larger number of evangelists, it is itself converted into an evangelist and consequently it starts spreading the information. The question is: How to choose a bounded cardinality initial set of evangelists so as to maximize the final number of influenced individuals? We prove that the problem is hard to solve, even in an approximate sense. On the positive side, we present exact polynomial time algorithms for trees and complete graphs. For general graphs, we derive exact parameterized algorithms. We also study the problem when the objective is to select a minimum number of evangelists capable of influencing the whole network. Our motivations to study these problems come from the areas of Viral Marketing and spread of influence in social networks. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 71(4), 346–357 2018