Abstract
One of the most elegant tools for understanding the behavior of a complex system of interacting entities is network analysis. Nevertheless, often such networks are incomplete because certain edges might be missing in the construction owing to limitations in data acquisition technologies. This is an ubiquitous problem for all application areas that use network analysis ranging from social networks to hyper-linked web networks to biological networks. As a result, an important question in analyzing such networks is how certain parameters get affected by varying levels of noise (i.e., percentage of missing edges). In this paper, we focus on two distinct types of parameters—community scoring functions and centrality measures and identify the effect of removal of edges in terms of (1) the sensitivity, that is how the parameter value changes as edges are removed, (2) the robustness, that is whether the network maintains certain structural features; specifically, we measure how well the change in structural features correlates with the change in the parameters, and (3) the reliability in the context of message spreading, that is how the time taken to broadcast a message changes as edges are removed; we measure how effective the parameters are for selecting the initiator node from which the message originates.We experiment using three noise models and various synthetic and real-world networks and test the effectiveness of the parameters; a majority of the outcomes are in favor of permanence thus making it the most effective metric. For the sensitivity experiments, permanence is the clear winner narrowly followed by closeness centrality. For robustness, permanence is highly correlated with both path based and spectral property based measures, which is remarkable considering its low computation cost compared to the other parameters. For the reliability experiments, closeness and betweenness centrality based initiator selection closely competes with permanence. Surprisingly permanence is a better parameter both in terms of sensitivity and reliability which are seemingly opposite in nature. This phenomena is due to a dual characteristic of permanence where the cumulative permanence over all vertices is sensitive to noise but the ids of the top-rank vertices, which are used to find initiators during message spreading remain relatively stable under noise. We discuss, in detail, how the joint community-like and centrality-like characteristic of permanence makes it an interesting metric for noisy graphs.
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Notes
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The results for the other two noise models are very similar and therefore not reported.
- 3.
Note the scale-size of the metrics is 2, 2, 1, 1 for permanence, modularity, conductance, and cut-ratio, respectively.
References
Biernacki, P., Waldorf, D.: Snowball sampling: problems and techniques of chain referral sampling. Sociol. Methods Res. 10(2), 141–163 (1981)
Booker, L.B.: The effects of observation errors on the attack vulnerability of complex networks. Technical report, DTIC Document (2012)
Borgatti, S.P., Carley, K.M., Krackhardt, D.: On the robustness of centrality measures under conditions of imperfect data. Soc. Netw. 28(2), 124–136 (2006)
Catanese, S.A., De Meo, P., Ferrara, E., Fiumara, G., Provetti, A.: Crawling facebook for social network analysis purposes. In: Proceedings of the International Conference on Web Intelligence, Mining and Semantics, p. 52. ACM, New York (2011)
Chakraborty, T., Srinivasan, S., Ganguly, N., Mukherjee, A., Bhowmick, S.: On the permanence of vertices in network communities. In: Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1396–1405. ACM, New York (2014)
Chierichetti, F., Lattanzi, S., Panconesi, A.: Rumour spreading and graph conductance. In: SODA, pp. 1657–1663. SIAM, Philadelphia (2010)
Fiedler, M.: Algebraic connectivity of graphs. Czechoslov. Math. J. 23(2), 298–305 (1973)
Ghosh, S., Banerjee, A., Sharma, N., Agarwal, S., Ganguly, N., Bhattacharya, S., Mukherjee, A.: Statistical analysis of the Indian railway network: a complex network approach. Acta Phys. Pol. B Proc. Suppl. 4(2), 123–138 (2011)
Girvan, M., Newman, M.E.: Community structure in social and biological networks. Proc. Natl. Acad. Sci. 99(12), 7821–7826 (2002)
Gower, J.C., et al.: Measures of similarity, dissimilarity and distance. Encycl. Stat. Sci. 5(397–405), 3 (1985)
Kim, M., Leskovec, J.: The network completion problem: inferring missing nodes and edges in networks. In: SDM, pp. 47–58. SIAM, Philadelphia (2011)
Kossinets, G.: Effects of missing data in social networks. Soc. Netw. 28(3), 247–268 (2006)
Lancichinetti, A., Fortunato, S.: Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities. Phys. Rev. E 80(1), 016118 (2009)
Laumann, E.O., Marsden, P.V., Prensky, D.: The boundary specification problem in network analysis. Res. Methods Soc. Netw. Anal. 61, 87 (1989)
Leskovec, J., Lang, K.J., Mahoney, M.: Empirical comparison of algorithms for network community detection. In: Proceedings of the 19th International Conference on World Wide Web, pp. 631–640. ACM, New York (2010)
Liu, J., Aggarwal, C., Han, J.: On integrating network and community discovery. In: Proceedings of the Eighth ACM International Conference on Web Search and Data Mining, pp. 117–126. ACM, New York (2015)
Mitchell, M.: Complex systems: network thinking. Artif. Intell. 170, 1194–1212 (2006)
Moustafa, W.E., Kimmig, A., Deshpande, A., Getoor, L.: Subgraph pattern matching over uncertain graphs with identity linkage uncertainty. In: 2014 IEEE 30th International Conference on Data Engineering (ICDE), pp. 904–915. IEEE, New York (2014)
Mukherjee, A.P., Xu, P., Tirthapura, S.: Mining maximal cliques from an uncertain graph. arXiv preprint arXiv:1310.6780 (2013)
Newman, M.: Networks: An Introduction. Oxford University Press, Oxford (2010)
Pfeiffer J.J. III, Neville, J.: Methods to determine node centrality and clustering in graphs with uncertain structure. arXiv preprint arXiv:1104.0319 (2011)
Platig, J., Ott, E., Girvan, M.: Robustness of network measures to link errors. Phys. Rev. E 88(6), 062812 (2013)
Sarkar, S., Kumar, S., Bhowmick, S., Mukherjee, A.: Sensitivity and reliability in incomplete networks: centrality metrics to community scoring functions. In: 2016 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM), pp. 69–72. IEEE, New York (2016)
Scellato, S., Leontiadis, I., Mascolo, C., Basu, P., Zafer, M.: Understanding robustness of mobile networks through temporal network measures. In: 2011 Proceedings IEEE INFOCOM, pp. 1–5. IEEE, New York (2011)
Verroios, V., Garcia-Molina, H.: Entity resolution with crowd errors (2015)
Vesdapunt, N., Garcia-Molina, H.: Identifying users in social networks with limited information (2014)
Wang, L., Wang, J., Bi, Y., Wu, W., Xu, W., Lian, B.: Noise-tolerance community detection and evolution in dynamic social networks. J. Comb. Optim. 28(3), 600–612 (2014)
Wang, X., Koç, Y., Derrible, S., Ahmad, S.N., Kooij, R.E.: Quantifying the robustness of metro networks. arXiv preprint arXiv:1505.06664 (2015)
Yan, B., Gregory, S.: Finding missing edges and communities in incomplete networks. J. Phys. A 44, 495102 (2011)
Zhu, Y.X., Lü, L., Zhang, Q.M., Zhou, T.: Uncovering missing links with cold ends. Phys. A Stat. Mech. Appl. 391(22), 5769–5778 (2012)
Acknowledgements
SS and AM would like to acknowledge the financial support from the ITRA DISARM project from DeiTY. SB would like to acknowledge funding from NSF:CCF Award no.1533881.
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Sarkar, S., Kumar, S., Bhowmick, S., Mukherjee, A. (2018). Centrality and Community Scoring Functions in Incomplete Networks: Their Sensitivity, Robustness, and Reliability. In: Özyer, T., Alhajj, R. (eds) Machine Learning Techniques for Online Social Networks. Lecture Notes in Social Networks. Springer, Cham. https://doi.org/10.1007/978-3-319-89932-9_7
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