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识别高阶网络传播中最有影响力的节点

李江 刘影 王伟 周涛

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识别高阶网络传播中最有影响力的节点

李江, 刘影, 王伟, 周涛

Identifying influential nodes in spreading process in higher-order networks

Li Jiang, Liu Ying, Wang Wei, Zhou Tao
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  • 识别网络传播中最有影响力的节点是控制传播速度和范围的重要步骤, 有助于加速有益信息扩散, 抑制流行病、谣言和虚假信息的传播等. 已有研究主要基于描述点对交互的低阶复杂网络. 然而, 现实中个体间的交互不仅发生在点对之间, 也发生在3个及以上节点形成的群体中. 群体交互可利用高阶网络来刻画, 如单纯复形与超图. 本文研究单纯复形上最有影响力的传播者识别方法. 首先, 提出单纯复形上易感-感染-恢复(SIR)微观马尔可夫链方程组, 定量刻画单纯复形上的疾病传播动力学. 接下来利用微观马尔可夫链方程组计算传播动力学中节点被感染的概率. 基于网络结构与传播过程, 定义节点的传播中心性, 用于排序节点传播影响力. 在两类合成单纯复形与4个真实单纯复形上的仿真结果表明, 相比于现有高阶网络中心性和复杂网络中最优的中心性指标, 本文提出的传播中心性能更准确地识别高阶网络中最有影响力的传播者.
    Identifying influential nodes in spreading process in the network is an important step to control the speed and range of spreading, which can be used to accelerate the spread of beneficial information such as healthy behaviors, innovations and suppress the spread of epidemics, rumors and fake news. Existing researches on identification of influential spreaders are mostly based on low-order complex networks with pairwise interactions. However, interactions between individuals occur not only between pairwise nodes but also in groups of three or more nodes, which introduces complex mechanism of reinforcement and indirect influence. The higher-order networks such as simplicial complexes and hypergraphs, can describe features of interactions that go beyond the limitation of pairwise interactions. Currently, there are relatively few researches of identifying influential spreaders in higher-order networks. Some centralities of nodes such as higher-order degree centrality and eigenvector centrality are proposed, but they mostly consider only the network structure. As for identification of influential spreaders, the spreading influence of a node is closely related to the spreading process. In this paper, we work on identification of influential spreaders on simplicial complexes by taking both network structure and dynamical process into consideration. Firstly, we quantitatively describe the dynamics of disease spreading on simplicial complexes by using the Susceptible-Infected-Recovered microscopic Markov equations. Next, we use the microscopic Markov equations to calculate the probability that a node is infected in the spreading process, which is defined as the spreading centrality (SC) of nodes. This spreading centrality involves both the structure of simplicial complex and the dynamical process on it, and is then used to rank the spreading influence of nodes. Simulation results on two types of synthetic simplicial complexes and four real simplicial complexes show that compared with the existing centralities on higher-order networks and the optimal centralities of collective influence and nonbacktracking centrality in complex networks, the proposed spreading centrality can more accurately identify the most influential spreaders in simplicial complexes. In addition, we find that the probability of nodes infected is highly positively correlated with its influence, which is because disease preferentially reaches nodes with many contacts, who can in turn infect their many neighbors and become influential spreaders.
      通信作者: 刘影, shinningliu@163.com
    • 基金项目: 国家自然科学基金(批准号: 61802321, 61903266)、四川省科技计划项目重点研发计划(批准号: 2023YFG0129)和中国博士后科学基金特别资助(批准号: 2019T120829)资助的课题.
      Corresponding author: Liu Ying, shinningliu@163.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61802321, 61903266), the Science and Technology Program of Sichuan Province, China (Grant No. 2023YFG0129), and the China Postdoctoral Science Fundation-Special Fund (Grant No. 2019T120829).
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    Moreno Y, Nekovee M, Pacheco A F 2004 Phys. Rev. E 69 066130Google Scholar

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    Motter A E 2004 Phys. Rev. Lett. 93 098701Google Scholar

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    Li D, Fu B, Wang Y, Lu G, Berezin Y, Stanley H E, Havlin S 2014 Proc. Natl. Acad. Sci. 112 669

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    Kephart J O, Sorkin G B, Chess D M, White S R 1997 Sci. Am. 277 88

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    Hale T, Angrist N, Goldszmidt R, et al. 2023 Nat. Hum. Behav. 5 529Google Scholar

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    Rocha Y M, de Moura G A, Desidério G A, et al. 2023 J. Public Health 31 1007Google Scholar

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    Schäfer B, Witthaut D, Timme M, Latora V 2018 Nat. Commun. 9 1975Google Scholar

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    任晓龙, 吕琳媛 2014 科学通报 59 1175Google Scholar

    Ren X L, Lü L Y 2014 Sci. Bull. 59 1175Google Scholar

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    Yang K C, Pierri F, Hui P M, Axelrod D, Torres-Lugo C, Bryden J, Menczer F 2021 Big Data Soc. 8 1

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    Nielsen B F, Simonsen L, Sneppen K 2021 Phys. Rev. Lett. 126 118301Google Scholar

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    Freeman L C 1978 Soc. Networks 1 215Google Scholar

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    Lü L, Zhou T, Zhang Q M, Stanley H E 2016 Nat. Commun. 7 10168Google Scholar

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    Kitsak M, Gallos L K, Havlin S, Liljeros F, Muchnik L, Stanley H E, Makse H A 2010 Nat. Phys. 6 888Google Scholar

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    Morone F, Makse H A 2015 Nature 524 65Google Scholar

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    Sabidussi G 1966 Psychometrika 31 581Google Scholar

    [17]

    Freeman L C 1977 Sociometry 40 35Google Scholar

    [18]

    Estrada E, Rodríguez-Velázquez J A 2005 Phys. Rev. E 71 056103Google Scholar

    [19]

    Bonacich P, Lloyd P 2001 Soc. Networks 23 191Google Scholar

    [20]

    Brin S, Page L 1998 Comput. Netw. ISDN Syst. 30 107Google Scholar

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    Martin T, Zhang X, Newman M E J 2014 Phys. Rev. E 90 052808Google Scholar

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    Lü L, Chen D, Ren X L, et al. 2016 Phys. Rep. 650 1Google Scholar

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    汪亭亭, 梁宗文, 张若曦 2023 物理学报 72 048901Google Scholar

    Wang T T, Liang Z W, Zhang R X 2023 Acta Phys. Sin. 72 048901Google Scholar

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    Maji G, Namtirtha A, Dutta A, Malta M C 2020 Exp. Syst. Appl. 144 113092Google Scholar

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    Liu J Q, Li X R, Dong J C 2021 Sci. China Technol. Sci. 64 451Google Scholar

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    Liu Y, Zeng Q, Pan L, Tang M 2023 IEEE Trans. Netw. Sci. Eng. 10 2201Google Scholar

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    Fan T, Lü L, Shi D, Zhou T 2021 Commun. Phys. 4 272Google Scholar

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    阮逸润, 老松杨, 汤俊, 白亮, 郭延明 2022 物理学报 71 176401Google Scholar

    Ruan Y R, Lao S Y, Tang J, Bai L, Guo Y M 2022 Acta Phys. Sin. 71 176401Google Scholar

    [29]

    Lung R I, Gaskó N, Suciu M A 2018 Scientometrics 117 1361Google Scholar

    [30]

    Iacopini I, Petri G, Barrat A, Latora V 2019 Nat. Commun. 10 2485Google Scholar

    [31]

    Battiston F, Cencetti G, Iacopini I, Latora V, Lucas M, Patania A, Young J G, Petri G 2020 Phys. Rep. 874 1Google Scholar

    [32]

    de Arruda G F, Petri G, Moreno Y 2020 Phys. Rev. Res. 2 023032Google Scholar

    [33]

    Wang W, Liu Q H, Liang J, Hu Y, Zhou T 2019 Phys. Rep. 820 1Google Scholar

    [34]

    Li W Y, Xue X, Pan L, Lin T, Wang W 2022 Appl. Math. Comput. 412 126595

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    Liu J G, Lin J H, Guo Q, Zhou T 2016 Sci. Rep. 6 21380Google Scholar

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    Zeng Q, Liu Y, Tang M, Gong J 2021 Knowledge-Based Syst. 229 107365Google Scholar

    [41]

    Li W, Nie Y, Li W, Chen X, Su S, Wang W 2022 Chaos 32 093135Google Scholar

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    Wang H, Ma C, Chen H S, Lai Y C, Zhang H F 2022 Nat. Commun. 13 3043Google Scholar

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    Génois M, Barrat A 2018 Epj Data Sci. 7 11Google Scholar

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    Isella L, Stehlé J, Barrat A, Cattuto C, Pinton J F, Van den Broeck W 2011 J. Theor. Biol. 271 166Google Scholar

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    Vanhems P, Barrat A, Cattuto C, Pinton J F, Khanafer N, Régis C, Kim B, Comte B, Voirin N 2013 PloS One 8 e73970Google Scholar

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  • 图 1  单纯复形上SIR传播过程 (a)—(j) 传播过程; (k) 恢复过程

    Fig. 1.  SIR spreading process on simplicial complex: (a)–(j) Spreading process; (k) recovery process.

    图 2  节点传播中心性与传播影响力的散点图. $ \overline{{{\mathrm{SC}}}} $与$ \overline{{{\mathrm{S}}}} $分别表示归一化后的节点传播中心性与传播影响力 (a) RSC; (b) SFSC; (c) InVS15; (d) LH10; (e) SFHH; (f) Thiers13

    Fig. 2.  Scatter plots of the spreaing centrality and spreaing influence of nodes. $ \overline{{{\mathrm{SC}}}} $ and $ {\overline{{\mathrm{S}}}} $ represent the normalized spreading centrality and spreading influence of nodes: (a) RSC; (b) SFSC; (c) InVS15; (d) LH10; (e) SFHH; (f) Thiers13.

    图 3  各中心性的不准确函数 (a) RSC; (b) SFSC; (c) InVS15; (d) LH10; (e) SFHH; (f) Thiers13

    Fig. 3.  Imprecisions of the centralities: (a) RSC; (b) SFSC; (c) InVS15; (d) LH10; (e) SFHH; (f) Thiers13

    图 4  不同1阶单纯形传播速率$ \beta_1=\alpha\beta_1^{\mathrm{c}} $下, 节点各中心性与传播影响力的肯德尔相关系数 (a) RSC; (b) SFSC; (c) InVS15; (d) LH10; (e) SFHH; (f) Thiers13

    Fig. 4.  Kendall’s tau correlation of the centralities and the spreading influence of nodes under different 1-simplex spreading rates $ \beta_1=\alpha\beta_1^{\mathrm{c}} $: (a) RSC; (b) SFSC; (c) InVS15; (d) LH10; (e) SFHH; (f) Thiers13

    图 5  不同2阶单纯形传播速率$ \beta_2 $下, 节点各中心性与传播影响力的肯德尔相关系数 (a) RSC; (b) SFSC; (c) InVS15; (d) LH10; (e) SFHH; (f) Thiers13

    Fig. 5.  Kendall’s tau correlation of the centralities and the spreading influence of nodes under different 2-simplex spreading rates $ \beta_2 $: (a) RSC; (b) SFSC; (c) InVS15; (d) LH10; (e) SFHH; (f) Thiers13

    表 1  合成与真实单纯复形属性

    Table 1.  Properties of the synthetic and real simplicial complexes

    网络 N $\langle k_1\rangle$ $\langle k_2\rangle$ $\beta_1^{\mathrm{c}}$
    RSC 2000 20 6 0.045
    SFSC 5000 16 5 0.049
    InVS15 213 20.19 7.94 0.040
    LH10 72 15.94 13.04 0.042
    SFHH 403 23.73 8.87 0.026
    Thiers13 326 18.10 12.15 0.048
    下载: 导出CSV

    表 2  各中心性的Top-K准确率

    Table 2.  Top-K accuracy of centralities

    网络 $K = 10$ $K = 20$ $K = 30$
    $ \mathrm{CI} $ $ \mathrm{NB} $ $ \mathrm{Deg} $ $ \mathrm{EVH} $ $ \mathrm{\mathrm{\mathrm{\mathrm{SC}\mathrm{ }}}} $ $ \mathrm{\mathrm{CI}} $ $ \mathrm{NB} $ $ \mathrm{Deg} $ $ \mathrm{\mathrm{EVH}} $ $ \mathrm{SC} $ $ \mathrm{CI} $ $ \mathrm{NB} $ $ \mathrm{\mathrm{Deg}} $ $ \mathrm{EVH} $ $ \mathrm{SC} $
    RSC 0.60 0.60 0.50 0.60 0.60 0.70 0.75 0.60 0.75 0.75 0.70 0.77 0.57 0.77 0.73
    SFSC 0.90 0.90 1.00 0.90 0.90 0.95 1.00 0.90 0.95 0.95 0.93 0.97 0.87 0.93 0.97
    InVS15 0.40 0.90 0.50 0.70 0.90 0.65 0.90 0.70 0.90 0.90 0.77 0.97 0.70 0.83 0.90
    LH10 0.10 1.00 0.90 0.90 0.90 0.55 0.95 0.90 0.95 0.95 0.87 1.00 0.93 0.97 1.00
    SFHH 0.80 0.90 0.60 0.70 0.90 0.85 0.90 0.70 0.90 0.90 0.87 0.93 0.77 0.87 0.90
    Thiers13 0.30 0.30 0.50 0.10 0.70 0.40 0.40 0.40 0.40 0.70 0.37 0.50 0.43 0.50 0.83
    下载: 导出CSV
  • [1]

    Pastor-Satorras R, Vespignani A 2001 Phys. Rev. Lett. 86 3200Google Scholar

    [2]

    Moreno Y, Nekovee M, Pacheco A F 2004 Phys. Rev. E 69 066130Google Scholar

    [3]

    Motter A E 2004 Phys. Rev. Lett. 93 098701Google Scholar

    [4]

    Li D, Fu B, Wang Y, Lu G, Berezin Y, Stanley H E, Havlin S 2014 Proc. Natl. Acad. Sci. 112 669

    [5]

    Kephart J O, Sorkin G B, Chess D M, White S R 1997 Sci. Am. 277 88

    [6]

    Hale T, Angrist N, Goldszmidt R, et al. 2023 Nat. Hum. Behav. 5 529Google Scholar

    [7]

    Rocha Y M, de Moura G A, Desidério G A, et al. 2023 J. Public Health 31 1007Google Scholar

    [8]

    Schäfer B, Witthaut D, Timme M, Latora V 2018 Nat. Commun. 9 1975Google Scholar

    [9]

    任晓龙, 吕琳媛 2014 科学通报 59 1175Google Scholar

    Ren X L, Lü L Y 2014 Sci. Bull. 59 1175Google Scholar

    [10]

    Yang K C, Pierri F, Hui P M, Axelrod D, Torres-Lugo C, Bryden J, Menczer F 2021 Big Data Soc. 8 1

    [11]

    Nielsen B F, Simonsen L, Sneppen K 2021 Phys. Rev. Lett. 126 118301Google Scholar

    [12]

    Freeman L C 1978 Soc. Networks 1 215Google Scholar

    [13]

    Lü L, Zhou T, Zhang Q M, Stanley H E 2016 Nat. Commun. 7 10168Google Scholar

    [14]

    Kitsak M, Gallos L K, Havlin S, Liljeros F, Muchnik L, Stanley H E, Makse H A 2010 Nat. Phys. 6 888Google Scholar

    [15]

    Morone F, Makse H A 2015 Nature 524 65Google Scholar

    [16]

    Sabidussi G 1966 Psychometrika 31 581Google Scholar

    [17]

    Freeman L C 1977 Sociometry 40 35Google Scholar

    [18]

    Estrada E, Rodríguez-Velázquez J A 2005 Phys. Rev. E 71 056103Google Scholar

    [19]

    Bonacich P, Lloyd P 2001 Soc. Networks 23 191Google Scholar

    [20]

    Brin S, Page L 1998 Comput. Netw. ISDN Syst. 30 107Google Scholar

    [21]

    Martin T, Zhang X, Newman M E J 2014 Phys. Rev. E 90 052808Google Scholar

    [22]

    Lü L, Chen D, Ren X L, et al. 2016 Phys. Rep. 650 1Google Scholar

    [23]

    汪亭亭, 梁宗文, 张若曦 2023 物理学报 72 048901Google Scholar

    Wang T T, Liang Z W, Zhang R X 2023 Acta Phys. Sin. 72 048901Google Scholar

    [24]

    Maji G, Namtirtha A, Dutta A, Malta M C 2020 Exp. Syst. Appl. 144 113092Google Scholar

    [25]

    Liu J Q, Li X R, Dong J C 2021 Sci. China Technol. Sci. 64 451Google Scholar

    [26]

    Liu Y, Zeng Q, Pan L, Tang M 2023 IEEE Trans. Netw. Sci. Eng. 10 2201Google Scholar

    [27]

    Fan T, Lü L, Shi D, Zhou T 2021 Commun. Phys. 4 272Google Scholar

    [28]

    阮逸润, 老松杨, 汤俊, 白亮, 郭延明 2022 物理学报 71 176401Google Scholar

    Ruan Y R, Lao S Y, Tang J, Bai L, Guo Y M 2022 Acta Phys. Sin. 71 176401Google Scholar

    [29]

    Lung R I, Gaskó N, Suciu M A 2018 Scientometrics 117 1361Google Scholar

    [30]

    Iacopini I, Petri G, Barrat A, Latora V 2019 Nat. Commun. 10 2485Google Scholar

    [31]

    Battiston F, Cencetti G, Iacopini I, Latora V, Lucas M, Patania A, Young J G, Petri G 2020 Phys. Rep. 874 1Google Scholar

    [32]

    de Arruda G F, Petri G, Moreno Y 2020 Phys. Rev. Res. 2 023032Google Scholar

    [33]

    Wang W, Liu Q H, Liang J, Hu Y, Zhou T 2019 Phys. Rep. 820 1Google Scholar

    [34]

    Li W Y, Xue X, Pan L, Lin T, Wang W 2022 Appl. Math. Comput. 412 126595

    [35]

    Fan J, Yin Q, Xia C, Perc M 2022 Proc. R. Soc. A. 478 20220059Google Scholar

    [36]

    Estrada E, Ross G J 2018 J. Theor. Biol. 438 46Google Scholar

    [37]

    Tudisco F, Higham D J 2021 Commun. Phys. 4 201Google Scholar

    [38]

    Kovalenko K, Romance M, Vasilyeva E, et al. 2022 Chaos Solitons Fractals 162 112397Google Scholar

    [39]

    Liu J G, Lin J H, Guo Q, Zhou T 2016 Sci. Rep. 6 21380Google Scholar

    [40]

    Zeng Q, Liu Y, Tang M, Gong J 2021 Knowledge-Based Syst. 229 107365Google Scholar

    [41]

    Li W, Nie Y, Li W, Chen X, Su S, Wang W 2022 Chaos 32 093135Google Scholar

    [42]

    Wang H, Ma C, Chen H S, Lai Y C, Zhang H F 2022 Nat. Commun. 13 3043Google Scholar

    [43]

    Génois M, Barrat A 2018 Epj Data Sci. 7 11Google Scholar

    [44]

    Isella L, Stehlé J, Barrat A, Cattuto C, Pinton J F, Van den Broeck W 2011 J. Theor. Biol. 271 166Google Scholar

    [45]

    Vanhems P, Barrat A, Cattuto C, Pinton J F, Khanafer N, Régis C, Kim B, Comte B, Voirin N 2013 PloS One 8 e73970Google Scholar

    [46]

    Mastrandrea R, Fournet J, Barrat A 2015 PloS One 10 e0136497Google Scholar

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  • PDF下载量:  52
  • 被引次数: 0
出版历程
  • 收稿日期:  2023-09-01
  • 修回日期:  2023-10-31
  • 上网日期:  2023-11-29
  • 刊出日期:  2024-02-20

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