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Influence Spread in Social Networks with both Positive and Negative Influences

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Computing and Combinatorics (COCOON 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10392))

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Abstract

Social networks are important mediums for spreading information, ideas, and influences among individuals. Most of existing research works of social networks focus on understanding the characteristics of social networks and spreading information through the “word of mouth” effect. However, most of them ignore negative influences among individuals and groups. Motivated by alleviating social problems, such as drinking, smoking, gambling, and influence spreading problems such as promoting new products, we take both positive and negative influences into consideration and propose a new optimization problem, named the Minimum-sized Positive Influential Node Set (MPINS) selection, to identify the minimum set of influential nodes, such that every node in the network can be positively influenced by these selected nodes no less than a threshold \(\theta \). Our contributions are threefold. First, we prove that, under the independent cascade model considering both positive and negative influences, MPINS is APX-hard. Subsequently, we present a greedy approximation algorithm to address the MPINS selection problem. Finally, to validate the proposed greedy algorithm, extensive simulations and experiments are conducted on random Graphs and seven different real-world data sets representing small, medium, and large scale networks.

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Notes

  1. 1.

    This model is reasonable since many empirical studies have analyzed the social influence probabilities between nodes [10, 17, 20].

  2. 2.

    A vertex cover is defined as a subset of nodes in a graph \(\mathcal {G}\) such that each edge of the graph is incident to at least one vertex of the set.

  3. 3.

    MIS can be defined formally as follows: given a graph \(G = (V,E)\), an Independent Set (IS) is a subset \(I \subset V\) such that for any two vertex \(v_{1}, v_{2} \in I\), they are not adjacent, i.e., \((v_{1}, v_{2}) \notin E\). An IS is called an MIS if we add one more arbitrary node to this subset, the new subset will not be an IS any more.

  4. 4.

    If there is a tie on the \(f(\mathcal {I})\) value, we use the node ID to break the tie.

  5. 5.

    http://snap.stanford.edu/data/.

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Acknowledgment

This research is funded in part by the Kennesaw State University College of Science and Mathematics Interdisciplinary Research Opportunities (IDROP) Program, the Provincial Key Research and Development Program of Zhejiang, China under No. 2016C01G2010916, the Fundamental Research Funds for the Central Universities, the Alibaba-Zhejiang University Joint Research Institute for Frontier Technologies (A.Z.F.T.) under Program No. XT622017000118, and the CCF-Tencent Open Research Fund under No. AGR20160109.

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Authors and Affiliations

  1. Department of Computer Science, Kennesaw State University, Marietta, GA, 30060, USA

    Jing (Selena) He & Ying Xie

  2. College of Computer Science and Technology, Zhejiang University, Hangzhou, China

    Shouling Ji

  3. Alibaba Group, Hangzhou, China

    Tianyu Du & Zhao Li

Authors
  1. Jing (Selena) He
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  2. Ying Xie
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  3. Tianyu Du
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  4. Shouling Ji
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  5. Zhao Li
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Correspondence to Shouling Ji .

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Editors and Affiliations

  1. Department of Computing, Hong Kong Polytechnic University, Hong Kong, China

    Yixin Cao

  2. Texas A&M University, College Station, Texas, USA

    Jianer Chen

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He, J.(., Xie, Y., Du, T., Ji, S., Li, Z. (2017). Influence Spread in Social Networks with both Positive and Negative Influences. In: Cao, Y., Chen, J. (eds) Computing and Combinatorics. COCOON 2017. Lecture Notes in Computer Science(), vol 10392. Springer, Cham. https://doi.org/10.1007/978-3-319-62389-4_51

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  • DOI: https://doi.org/10.1007/978-3-319-62389-4_51

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