Research article

A measure of identifying influential community based on the state of critical functionality

  • Received: 02 August 2020 Accepted: 09 October 2020 Published: 22 October 2020
  • As an open issue, the measure of community influential is no uniform standard, how to measure the influence of community has attracted extensive attention. This paper proposed a quantitative measure to identify the influence of community. Based on the state of critical functionality (SCF), a new function, which names as the weighted state of critical functionality (WSCF), is defined. For the WSCF, not only the connections among communities but also the topology within community is considered. When the community structure of the complex network is divided, each community is renormalized as a node by the renormalization method. Then, the influence of community is measured by the values of WSCF, the greater the value of WSCF, the less the influence of the corresponding community. The influence of community of three classic constructed networks (i.e., a Erodös-Rényi (ER) random network, a BA scale free network and a small-word (SW) network) is measured by the proposed method. To further verify the feasibility of the method, two community detection algorithms are used to divide community structure in the real networks. The influence of the community of the 9/11 terrorist network, a US Air network and a PolBooks network is measured by the proposed method. The influence of each community could be measured and the most influential community in each network is identified by the proposed method. The results reveal that the proposed method is a feasible measure to identify the influence of community, its recognition effect is better than SCF, and accuracy is higher. The SCF is a special case of WSCF, when the weights and cluster coefficients are equal to 1. For the proposed method, once the community structure of the network is divided, the corresponding community influence is identified by the proposed method, which is not affected by the community division algorithms.

    Citation: Mingli Lei, Daijun Wei. A measure of identifying influential community based on the state of critical functionality[J]. Mathematical Biosciences and Engineering, 2020, 17(6): 7167-7191. doi: 10.3934/mbe.2020368

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  • As an open issue, the measure of community influential is no uniform standard, how to measure the influence of community has attracted extensive attention. This paper proposed a quantitative measure to identify the influence of community. Based on the state of critical functionality (SCF), a new function, which names as the weighted state of critical functionality (WSCF), is defined. For the WSCF, not only the connections among communities but also the topology within community is considered. When the community structure of the complex network is divided, each community is renormalized as a node by the renormalization method. Then, the influence of community is measured by the values of WSCF, the greater the value of WSCF, the less the influence of the corresponding community. The influence of community of three classic constructed networks (i.e., a Erodös-Rényi (ER) random network, a BA scale free network and a small-word (SW) network) is measured by the proposed method. To further verify the feasibility of the method, two community detection algorithms are used to divide community structure in the real networks. The influence of the community of the 9/11 terrorist network, a US Air network and a PolBooks network is measured by the proposed method. The influence of each community could be measured and the most influential community in each network is identified by the proposed method. The results reveal that the proposed method is a feasible measure to identify the influence of community, its recognition effect is better than SCF, and accuracy is higher. The SCF is a special case of WSCF, when the weights and cluster coefficients are equal to 1. For the proposed method, once the community structure of the network is divided, the corresponding community influence is identified by the proposed method, which is not affected by the community division algorithms.


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    [1] A. Clauset, M. E. J. Newman, C. Moore, Finding community structure in very large networks, Phys. Rev. E, 70 (2004), 066111.
    [2] Y. Deng, Uncertainty measure in evidence theory, Sci. China Inf. Sci., 64 (2021), http://10.1007/s11432--020--3006--9.
    [3] J. Ramirez Marquez, M. Claudio, Vulnerability metrics and analysis for communities in complex networks, Reliab. Eng. Syst. Saf., 96 (2011), 1360-1366.
    [4] Y. Zhang, M. K. Lindell, C. S. Prater, Vulnerability of community businesses to environmental disasters, Disasters, 33 (2009), 38-57.
    [5] M. Hu, X. Wang, X. Wen, Y. Xia, Microbial community structures in different wastewater treatment plants as revealed by 454-pyrosequencing analysis, Bioresour. Technol., 117 (2012), 72-79.
    [6] A. Tyakht, E. Kostryukova, A. Popenko, M. Belenikin, A. Pavlenko, A. Larin, et al., Human gut microbiota community structures in urban and rural populations in russia, Nat. Commun., 4 (2014), 1-9.
    [7] O. Koren, D. Knights, A. Gonzalez, L. Waldron, N. Segata, R. Knight, et al., A guide to enterotypes across the human body: meta-analysis of microbial community structures in human microbiome datasets, PLOS Comput. Biol., 9 (2013), e1002863.
    [8] B. H. Morrow, Identifying and mapping community vulnerability, Disasters, 23 (1999), 1-18.
    [9] M. Girvan, M. E. J. Newman, Community structure in social and biological networks, Proc. Natl. Acad. Sci. USA, 99 (2002), 7821-7826.
    [10] P. M. Gleiser, L. Danon, Community structure in jazz, Adv. Complex Syst., 6 (2003), 565-573.
    [11] M. E. J. Newman, M. Girvan, Finding and evaluating community structure in networks, Phys. Rev. E, 69 (2004), 026113.
    [12] S. Srinivas, C. Rajendran, Community detection and influential node identification in complex networks using mathematical programming, Expert Syst. Appl., 135 (2019), 296-312.
    [13] Z. H. Deng, H. H. Qiao, Q. Song, L. Gao, A complex network community detection algorithm based on label propagation and fuzzy c-means, Physica A, 519 (2019), 217-226.
    [14] F. Liu, Y. Deng, A fast algorithm for network forecasting time series, IEEE Access, 7 (2019), 102554-102560.
    [15] J. Zhao, H. Mo, Y. Deng, An efficient network method for time series forecasting based on the DC algorithm and visibility relation, IEEE Access, 8 (2020), http://10.1109/ACCESS.2020.2964067.
    [16] L. C. Freeman, A set of measures of centrality based on betweenness, Sociometry, 40 (1977), 35-41.
    [17] Z. Ghalmane, C. Cherifi, H. Cherifi, M. E. Hassouni, Centrality in complex networks with overlapping community structure, Sci. Rep., 9 (2019), 10133.
    [18] H. Cherifi, G. Palla, B. K. Szymanski, X. Lu, On community structure in complex networks: challenges and opportunities, Appl. Netw. Sci., 4 (2019), https://doi.org/10.1007/s41109-019-0238-9.
    [19] M. E. J. Newman, Fast algorithm for detecting community structure in networks, Phys. Rev. E, 69 (2004), 066133.
    [20] M. E. J. Newman, Modularityand community structure in networks, Proc. Natl. Acad. Sci. USA, 103 (2006), 8577-8582.
    [21] U. N. Raghavan, R. Albert, S. Kumara, Near linear time algorithm to detect community structures in large-scale networks, Phys. Rev. E, 76 (2007), 036106.
    [22] H. F. Zhou, J. Li, J. H. Li, F. C. Zhang, Y. A. Cui, A graph clustering method for community detection in complex networks, Physica A, 469 (2017), 551-562.
    [23] C. M. Rocco, J. Moronta, J. E. Ramirez-Marquez, K. Barker, Effects of multi-state links in network community detection, Reliab. Eng. Syst. Saf., 163 (2017), 46-56.
    [24] G. Cantin, C. J. Silva, Influence of the topology on the dynamics of a complex network of hiv/aids epidemic models, Math. Biosci. Eng., 4 (2019), 1145-1169.
    [25] M. Liu, S. He, Y. Sun, The impact of media converge on complex networks on disease transmission, Math. Biosci. Eng., 16 (2019), 6335-6349.
    [26] Z. Zhuang, Z. Lu, Z. Huang, C. Liu, W. Qin, A novel complex network based dynamic rule selection approach for open shop scheduling problem with release dates, Math. Biosci. Eng., 16 (2019), 4491-4505.
    [27] D. Wei, X. Zhang, S. Mahadevan, Measuring the vulnerability of community structure in complex networks, Reliab. Eng. Syst. Saf., 174 (2018), 41-52.
    [28] B. Sluban, J. Smailović, S. Battiston, I. Mozetič, Sentiment leaning of influential communities in social networks, Comput. Soc. Networks, 2 (2015), 9-29.
    [29] M. Lei, D. Wei, Identifying influence for community in complex networks, IEEE 30th CCDC, (2018), 5346-5349.
    [30] X. Wu, Z. Liu, How community structure influences epidemic spread in social networks, Physica A, 387 (2008), 623-630.
    [31] R. H. Li, L. Qin, J. X. Yu, R. Mao, Influential community search in large networks, Proc. VlDB Endow., 8 (2015), 509-520.
    [32] W. Chen, J. Liu, Z. Chen, J. Chen, A top-r k influential community search algorithm., Int. J. Performability Eng., 14 (2018), 2652-2662.
    [33] R. H. Li, L. Qin, J. X. Yu, R. Mao, Finding influential communities in massive networks, VLDB J., 26 (2017), 751-776.
    [34] J. Zhao, Y. Song, Y. Deng, A novel model to identify the influential nodes: Evidence Theory Centrality, IEEE Access, 8 (2020), 46773-46780.
    [35] S. Oldham, B. Fulcher, L. Parkes, A. Arnatkevicit, A. Fornito, Consistency and differences between centrality measures across distinct classes of networks, PloS One, 14 (2019), 1-23.
    [36] J. Zhao, Y. Wang, Y. Deng, Identifying influential nodes in complex networks from global perspective, Chaos Solitons Fract., 133 (2020), 109637.
    [37] M. Perc, O. Peek, S. M. Kamal, Impact of density and interconnectedness of influential players on social welfare, Appl. Math. Comput., 249 (2014), 19-23.
    [38] D. Chen, L. Lü, M. Shang, Y. Zhang, T. Zhou, Identifying influential nodes in complex networks, Physica A, 391 (2012), 1777-1787.
    [39] P. Bonacich, P. Lloyd, Eigenvector-like measures of centrality for asymmetric relations, Soc. Networks, 23 (2001), 191-201.
    [40] L. Lü, Y. Zhang, C. Yeung, T. Zhou, Leaders in social networks, the delicious case, PloS One, 6 (2011), 1-9.
    [41] D. Kempe, J. Kleinberg, E. Tardos, Influential nodes in a diffusion model for social networks, Lect. Notes Comput. Sci., 3580 (2005), 1127-1138.
    [42] M. Kimura, K. Saito, Tractable models for information diffusion in social networks, ECML PKDD, 4231 (2006), 259-271.
    [43] M. Kimura, K. Saito, R. Nakano, H. Motoda, Extracting influential nodes on a social network for information diffusion, Data Min. Knowl. Discov., 20 (2010), 70-97.
    [44] F. Liu, Z. Wang, Y. Deng, Gmm: A generalized mechanics model for identifying the importance of nodes in complex networks, Knowl. Based Syst., 193 (2020), 105464.
    [45] G. Yang, T. P. Benko, M. Cavaliere, J. Huang, M. Perc, Identification of influential invaders in evolutionary populations, Sci. Rep., 9 (2019), 7305-7317.
    [46] J. Zhao, Y. Song, F. Liu, Y. Deng, The identification of influential nodes based on structure similarity, Conn. Sci., 32 (2020), 1-18.
    [47] U. Bhatia, D. Kumar, E. Kodra, A. R. Ganguly, Network science based quantification of resilience demonstrated on the indian railways network, Plos One, 10 (2015), 1-17.
    [48] T. Wen, D. Pelusi, Y. Deng, Vital spreaders identification in complex networks with multi-local dimension, Knowl.Based Syst., 195 (2020), 105717.
    [49] Y. Zhao, S. Li, F. Jin, Identification of influential nodes in social networks with community structure based on label propagation, Neurocomput., 210 (2016), 33-44.
    [50] Z. Zhao, X. Wang, W. Zhang, Z. Zhu, A community-based approach to identifying influential spreaders, Entropy, 17 (2015), 2228-2252.
    [51] Z. Ghalmane, M. E. Hassouni, C. Cherifi, H. Cherifi, Centrality in modular networks, EPJ Data Sci., 8 (2019), 15.
    [52] J. E. Ramirez-Marquez, C. M. Rocco, K. Barker, J. Moronta, Quantifying the resilience of community structures in networks, Reliab. Eng. Syst. Saf., 169 (2018), 466-474.
    [53] P. Zhang, J. Wang, X. Li, M. Li, Z. Di, Y. Fan, Clustering coefficient and community structure of bipartite networks, Physica A, 387 (2008), 6869-6875.
    [54] R. A. Erdös P, On the evolution of random graphs, Publ. Math. Inst. Hung. Acad. Sci., 5 (1960), 15-27.
    [55] A. L. Barabási, R. Albert, Emergence of scaling in random networks, Science, 286 (1999), 509-512.
    [56] D. J. Watts, S. H. Strogatz, Collective dynamics of small-world networks, Nature, 393 (1998), 440-442.
    [57] V. E. Krebs, Mapping networks of terrorist cells, Connections, 24 (2002), 43-52.
    [58] V. Batagelj, A. Mrvar, Pajek datasets, 2006. Available from: http://vlado.fmf.uni-lj.si/pub/networks/data/mix/USAir97.net.
    [59] V. E. Krebs, Unpublished, 2007. Available from: http://www.orgnet.com/.
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