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Centralities for networks with consumable resources

Published online by Cambridge University Press:  13 September 2019

Hayato Ushijima-Mwesigwa Open the ORCID record for Hayato Ushijima-Mwesigwa [Opens in a new window] ,
Zadid Khan ,
Mashrur A. Chowdhury  and
Ilya Safro
Hayato Ushijima-Mwesigwa*
Affiliation:
School of Computing, Clemson University, Clemson, SC, USA
Zadid Khan
Affiliation:
Department of Civil Engineering, Clemson University, Clemson, SC, USA (emails: [email protected], [email protected])
Mashrur A. Chowdhury
Affiliation:
Department of Civil Engineering, Clemson University, Clemson, SC, USA (emails: [email protected], [email protected])
Ilya Safro
Affiliation:
School of Computing, Clemson University, Clemson, SC, USA (email: [email protected])
*
*Corresponding author. Email: [email protected]
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Abstract

Identification of influential nodes is an important step in understanding and controlling the dynamics of information, traffic, and spreading processes in networks. As a result, a number of centrality measures have been proposed and used across different application domains. At the heart of many of these measures lies an assumption describing the manner in which traffic (of information, social actors, particles, etc.) flows through the network. For example, some measures only count shortest paths while others consider random walks. This paper considers a spreading process in which a resource necessary for transit is partially consumed along the way while being refilled at special nodes on the network. Examples include fuel consumption of vehicles together with refueling stations, information loss during dissemination with error-correcting nodes, and consumption of ammunition of military troops while moving. We propose generalizations of the well-known measures of betweenness, random-walk betweenness, and Katz centralities to take such a spreading process with consumable resources into account. In order to validate the results, experiments on real-world networks are carried out by developing simulations based on well-known models such as Susceptible-Infected-Recovered and congestion with respect to particle hopping from vehicular flow theory. The simulation-based models are shown to be highly correlated with the proposed centrality measures.

Reproducibility: Our code and experiments are available at https://github.com/hmwesigwa/soc_centrality

Keywords

network centralityKatz centralitybetweenness centralityrandom-walk betweenness centralityconsumable resources
Type
Original Article
Information
Network Science , Volume 7 , Issue 3 , September 2019 , pp. 376 - 401
Copyright
© Cambridge University Press 2019 

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References

Albert, R., & Barabási, A-L. (2002). Statistical mechanics of complex networks. Reviews of Modern Physics, 74(1), 47.CrossRefGoogle Scholar
Albert, R., Jeong, H., & Barabási, A-L. (2000). Error and attack tolerance of complex networks. Nature, 406(6794), 378.CrossRefGoogle ScholarPubMed
Altshuler, Y., Puzis, R., Elovici, Y., Bekhor, S., & Pentland, A. S. (2011). Augmented betweenness centrality for mobility prediction in transportation networks. Paper presented at the International Workshop on Finding Patterns of Human Behaviors in Networks and Mobility Data, nemo11.Google Scholar
Bae, J., & Kim, S. (2014). Identifying and ranking influential spreaders in complex networks by neighborhood coreness. Physica A: Statistical Mechanics and Its Applications, 395, 549–559.CrossRefGoogle Scholar
Barrat, A., Barthelemy, M., & Vespignani, A. (2008). Dynamical processes on complex networks. Cambridge University Press.CrossRefGoogle Scholar
Basu, A., Fleming, S., Stanier, J., Naicken, S., Wakeman, I., & Gurbani, V. K. (2013). The state of peer-to-peer network simulators. ACM Computing Surveys (CSUR), 45(4), 46.CrossRefGoogle Scholar
Bavelas, A. (1948). A mathematical model for group structures. Human Organization, 7(3), 16–30.CrossRefGoogle Scholar
Bettencourt, L. M. A., Cintrón-Arias, A., Kaiser, D. I, & Castillo-Chávez, C. (2006). The power of a good idea: Quantitative modeling of the spread of ideas from epidemiological models. Physica A: Statistical Mechanics and Its Applications, 364, 513–536.CrossRefGoogle Scholar
Bi, Z., Kan, T., Mi, C. C., Zhang, Y., Zhao, Z., & Keoleian, G. A. (2016). A review of wireless power transfer for electric vehicles: Prospects to enhance sustainable mobility. Applied Energy, 179, 413–425.CrossRefGoogle Scholar
Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., & Hwang, D-U. (2006). Complex networks: Structure and dynamics. Physics Reports, 424(4–5), 175–308.CrossRefGoogle Scholar
Bonacich, P. (1987). Power and centrality: A family of measures. American Journal of Sociology, 92(5), 1170–1182.CrossRefGoogle Scholar
Bonacich, Phillip. (1991). Simultaneous group and individual centralities. Social Networks, 13(2), 155–168.CrossRefGoogle Scholar
Borgatti, S. P. (2005). Centrality and network flow. Social Networks, 27(1), 55–71.CrossRefGoogle Scholar
Brandes, U. (2001). A faster algorithm for betweenness centrality. Journal of Mathematical Sociology, 25(2), 163–177.CrossRefGoogle Scholar
Brandes, U., & Fleischer, D. (2005). Centrality measures based on current flow. STACS (vol. 3404, pp. 533–544). Berlin, Heidelberg: Springer.Google Scholar
Chen, J., & Safro, I. (2011). Algebraic distance on graphs. SIAM Journal on Scientific Computing, 33(6), 3468–3490.CrossRefGoogle Scholar
Chen, Z., He, F., & Yin, Y. (2016). Optimal deployment of charging lanes for electric vehicles in transportation networks. Transportation Research Part B: Methodological, 91, 344–365.CrossRefGoogle Scholar
Cirimele, V., Freschi, F., & Guglielmi, P. (2014). Wireless power transfer structure design for electric vehicle in charge while driving. 2014 International Conference on Electrical Machines (ICEM). IEEE (pp. 2461–2467).CrossRefGoogle Scholar
Cohen, R., Erez, K., Ben-Avraham, D., & Havlin, S. (2001). Breakdown of the internet under intentional attack. Physical Review Letters, 86(16), 3682.CrossRefGoogle ScholarPubMed
Colizza, V., Pastor-Satorras, R., & Vespignani, A. (2007). Reaction–diffusion processes and metapopulation models in heterogeneous networks. Nature Physics, 3(4), 276.CrossRefGoogle Scholar
Crucitti, P., Latora, V., & Porta, S. (2006). Centrality in networks of urban streets. Chaos: An Interdisciplinary Journal of Nonlinear Science, 16(1), 015113.CrossRefGoogle ScholarPubMed
Davis, T. A., & Hu, Y. (2011). The university of florida sparse matrix collection. ACM Transactions on Mathematical Software (TOMS), 38(1), 1.Google Scholar
Diekmann, O., & Heesterbeek, J. A. P. (2000). Mathematical epidemiology of infectious diseases: Model building, analysis and interpretation (Vol. 5). John Wiley & Sons.Google Scholar
Fouss, F., Pirotte, A., Renders, J-M., & Saerens, M. (2007). Random-walk computation of similarities between nodes of a graph with application to collaborative recommendation. IEEE Transactions on Knowledge and Data Engineering, 19(3), 355–369.CrossRefGoogle Scholar
Freeman, L. C. (1978). Centrality in social networks conceptual clarification. Social Networks, 1(3), 215–239.CrossRefGoogle Scholar
Freeman, L. C, Borgatti, S. P, & White, D. R. (1991). Centrality in valued graphs: A measure of betweenness based on network flow. Social Networks, 13(2), 141–154.CrossRefGoogle Scholar
Fuller, M. (2016). Wireless charging in california: Range, recharge, and vehicle electrification. Transportation Research Part C: Emerging Technologies, 67, 343–356.CrossRefGoogle Scholar
Ghosh, R., & Lerman, K. (2012). Rethinking centrality: The role of dynamical processes in social network analysis. arxiv preprint arxiv:1209.4616.Google Scholar
Guimerà, R., Díaz-Guilera, A., Vega-Redondo, F., Cabrales, A., & Arenas, A. (2002). Optimal network topologies for local search with congestion. Physical Review Letters, 89(24), 248701.CrossRefGoogle ScholarPubMed
Gutfraind, A., Safro, I., & Meyers, L. A. (2015). Multiscale network generation. 2015 18th international conference on information fusion (fusion) (pp. 158–165). IEEE.Google Scholar
Hethcote, H. W. (2000). The mathematics of infectious diseases. Siam Review, 42(4), 599–653.CrossRefGoogle Scholar
Holme, P. (2003). Congestion and centrality in traffic flow on complex networks. Advances in Complex Systems, 6(02), 163–176.CrossRefGoogle Scholar
Huisinga, T., Barlovic, R., Knospe, W., Schadschneider, A., & Schreckenberg, M. (2001). A microscopic model for packet transport in the internet. Physica A: Statistical Mechanics and Its Applications, 294(1–2), 249–256.CrossRefGoogle Scholar
Huitema, C. (2000). Routing in the internet. Prentice-Hall.Google Scholar
Interdonato, R., & Tagarelli, A. (2016). To trust or not to trust lurkers? Evaluation of lurking and trustworthiness in ranking problems. International conference and school on network science (pp. 43–56). Springer.Google Scholar
Jang, Y. J., Ko, Y. D., & Jeong, S. (2012). Optimal design of the wireless charging electric vehicle. 2012 IEEE international electric vehicle conference (IEVC) (pp. 1–5). IEEE.CrossRefGoogle Scholar
Jayasinghe, A., Sano, K., & Nishiuchi, H. (2015). Explaining traffic flow patterns using centrality measures. International Journal for Traffic and Transport Engineering, 5(2), 134–149.CrossRefGoogle Scholar
Jayaweera, I. M. L. N., Perera, K. K. K. R., & Munasinghe, J. (2017). Centrality measures to identify traffic congestion on road networks: A case study of Sri Lanka. IOSR Journal of Mathematics (IOSR-JM).CrossRefGoogle Scholar
Jiang, B., & Claramunt, C. (2004). A structural approach to the model generalization of an urban street network. Geoinformatica, 8(2), 157–171.CrossRefGoogle Scholar
Jiang, B., & Jia, T. (2011). Agent-based simulation of human movement shaped by the underlying street structure. International Journal of Geographical Information Science, 25(1), 51–64.CrossRefGoogle Scholar
Katz, J. (1998). Luring the lurkers. Retrieved march, 1(1999), 1999.Google Scholar
Katz, L. (1953). A new status index derived from sociometric analysis. Psychometrika, 18(1), 39–43.CrossRefGoogle Scholar
Keeling, M. J, & Rohani, P. (2011). Modeling infectious diseases in humans and animals. Princeton University Press.CrossRefGoogle Scholar
Kendall, M. G. (1938). A new measure of rank correlation. Biometrika, 30(1/2), 81–93.CrossRefGoogle Scholar
Kephart, J. O, Sorkin, G. B, Chess, D. M, & White, S. R. (1997). Fighting computer viruses. Scientific American, 277(5), 88–93.CrossRefGoogle Scholar
Khan, M. D., Chowdhury, M., Khan, S. M., Safro, I., & Ushijima-Mwesigwa, H. (2018). Utility maximization framework for opportunistic wireless electric vehicle charging. Paper presented at Transportation Research Board 97th Annual Meeting, Transportation Research Board.Google Scholar
Khan, Z., Khan, S. M., Chowdhury, M., Safro, I., & Ushijima-Mwesigwa, H. (2019). Wireless charging utility maximization and intersection control delay minimization framework for electric vehicles. Computer-Aided Civil and Infrastructure Engineering.CrossRefGoogle Scholar
Kitsak, M., Gallos, L. K., Havlin, S., Liljeros, F., Muchnik, L., Stanley, H. E., & Makse, H. A. (2010). Identification of influential spreaders in complex networks. Nature Physics, 6(11), 888.CrossRefGoogle Scholar
Kleinfeld, J. S. (2002). The small world problem. Society, 39(2), 61–66.CrossRefGoogle Scholar
Klemm, K., Serrano, M. Á., Eguíluz, V. M, & San Miguel, M. (2012). A measure of individual role in collective dynamics. Scientific Reports, 2, 292.CrossRefGoogle ScholarPubMed
Lai, H-M., & Chen, T. T. (2014). Knowledge sharing in interest online communities: A comparison of posters and lurkers. Computers in Human Behavior, 35, 295–306.CrossRefGoogle Scholar
Leskovec, J., Adamic, L. A., & Huberman, B. A. (2007a). The dynamics of viral marketing. ACM Transactions on the Web (TWEB), 1(1), 5.CrossRefGoogle Scholar
Leskovec, J., Kleinberg, J., & Faloutsos, C. (2007b). Graph evolution: Densification and shrinking diameters. ACM Transactions on Knowledge Discovery from Data (TKDD), 1(1), 2.CrossRefGoogle Scholar
Li, D., Fu, B., Wang, Y., Lu, G., Berezin, Y., Stanley, H. E., & Havlin, S. (2015). Percolation transition in dynamical traffic network with evolving critical bottlenecks. Proceedings of the National Academy of Sciences, 112(3), 669–672.CrossRefGoogle ScholarPubMed
Li, S., & Mi, C. C. (2015). Wireless power transfer for electric vehicle applications. IEEE Journal of Emerging and Selected Topics in Power Electronics, 3(1), 4–17.Google Scholar
Liu, F., Ren, Y., & Shan, X. M. (2002). A simple cellular automata model for packet transport in the internet. Acta Physica Sinica, 51(6), 1175–1180.Google Scholar
Liu, J-G., Wu, Z-X., & Wang, F. (2007). Opinion spreading and consensus formation on square lattice. International Journal of Modern Physics C, 18(07), 1087–1094.CrossRefGoogle Scholar
Liu, J-G., Lin, J-H., Guo, Q., & Zhou, T. (2016). Locating influential nodes via dynamics-sensitive centrality. Scientific Reports, 6, 21380.CrossRefGoogle ScholarPubMed
Lukic, S., & Pantic, Z. (2013). Cutting the cord: Static and dynamic inductive wireless charging of electric vehicles. IEEE Electrification Magazine, 1(1), 57–64.CrossRefGoogle Scholar
Marett, K., & Joshi, K. D. (2009). The decision to share information and rumors: Examining the role of motivation in an online discussion forum. Communications of the Association for Information Systems, 24(1), 4.CrossRefGoogle Scholar
Mason, B. (1999). Issues in virtual ethnography. Ethnographic studies in real and virtual environments: Inhabited information spaces and connected communities (pp. 61–69).Google Scholar
Moreno, Y., Nekovee, M., & Pacheco, A. F. (2004). Dynamics of rumor spreading in complex networks. Physical Review E, 69(6), 066130.CrossRefGoogle ScholarPubMed
Motter, A. E. (2004). Cascade control and defense in complex networks. Physical Review Letters, 93(9), 098701.CrossRefGoogle ScholarPubMed
Nagel, K. (1996). Particle hopping models and traffic flow theory. Physical Review E, 53(5), 4655.CrossRefGoogle ScholarPubMed
Newman, M. E. J. (2003). The structure and function of complex networks. Siam Review, 45(2), 167–256.CrossRefGoogle Scholar
Newman, M. E. J. (2005). A measure of betweenness centrality based on random walks. Social Networks, 27(1), 39–54.CrossRefGoogle Scholar
Ning, P., Miller, J. M., Onar, O. C., & White, C. P. (2013). A compact wireless charging system for electric vehicles. 2013 IEEE energy conversion congress and exposition (ECCE). IEEE (pp. 3629–3634).CrossRefGoogle Scholar
Page, L., Brin, S., Motwani, R., & Winograd, T. (1999). The pagerank citation ranking: Bringing order to the web. Tech. Rept. Stanford InfoLab.Google Scholar
Park, K., & Yilmaz, A. (2010). A social network analysis approach to analyze road networks. Paper presented at ASPRS Annual Conference. San Diego, CA.Google Scholar
Pastor-Satorras, R., & Vespignani, A. (2001). Epidemic spreading in scale-free networks. Physical Review Letters, 86(14), 3200.CrossRefGoogle ScholarPubMed
Porta, S., Crucitti, P., & Latora, V. (2006). The network analysis of urban streets: a primal approach. Environment and Planning B: Planning and Design, 33(5), 705–725.CrossRefGoogle Scholar
Preece, J., Nonnecke, B., & Andrews, D. (2004). The top five reasons for lurking: improving community experiences for everyone. Computers in Human Behavior, 20(2), 201–223.CrossRefGoogle Scholar
Qiu, C., Chau, K. T., Liu, C., & Chan, C. C. (2013). Overview of wireless power transfer for electric vehicle charging. 2013 world electric vehicle symposium and exhibition (EVS27). IEEE (pp. 1–9).CrossRefGoogle Scholar
Riemann, R., Wang, D. Z. W., & Busch, F. (2015). Optimal location of wireless charging facilities for electric vehicles: Flow-capturing location model with stochastic user equilibrium. Transportation Research Part C: Emerging Technologies, 58, 1–12.CrossRefGoogle Scholar
Ripeanu, M., & Foster, I. (2002). Mapping the Gnutella network: Macroscopic properties of large-scale peer-to-peer systems. International workshop on peer-to-peer systems (pp. 85–93). Springer.CrossRefGoogle Scholar
Rossi, R., & Ahmed, N. (2015). The network data repository with interactive graph analytics and visualization. AAAI (vol. 15, pp. 4292–4293).Google Scholar
Scheurer, J., Curtis, C., & Porta, S. (2008). Spatial network analysis of multimodal transport systems: Developing a strategic planning tool to assess the congruence of movement and urban structure: a case study of perth before and after the perth-to-mandurah railway. Paper presented at GAMUT, Australasian Centre for the Governance and Management of Urban Transport, University of Melbourne.Google Scholar
Schlosser, A. E. (2005). Posting versus lurking: Communicating in a multiple audience context. Journal of Consumer Research, 32(2), 260–265.CrossRefGoogle Scholar
Shaydulin, R., Chen, J., & Safro, I. (2017). Relaxation-based coarsening for multilevel hypergraph partitioning. SIAM Multiscale Modeling and Simulation, preprint arxiv:1710.06552.Google Scholar
Šikić, M., Lančić, A., Antulov-Fantulin, N., & Štefančić, H. (2013). Epidemic centralities there an underestimated epidemic impact of network peripheral nodes? The European Physical Journal B, 86(10), 440.CrossRefGoogle Scholar
Soroka, V., Jacovi, M., & Ur, S. (2003). We can see you: a study of communities invisible people through reachout. Communities and technologies (pp. 65–79). Springer.CrossRefGoogle Scholar
Southworth, M., & Ben-Joseph, E. (2013). Streets and the shaping of towns and cities. Island Press.Google Scholar
Spring, N., Mahajan, R., & Wetherall, D. (2002). Measuring ISP topologies with rocketfuel. SIGCOMM (vol. 32, pp. 133–145).CrossRefGoogle Scholar
Staudt, C. L., Hamann, M., Gutfraind, A., Safro, I., & Meyerhenke, H. (2017). Generating realistic scaled complex networks. Applied Network Science, 2(1), 36.CrossRefGoogle ScholarPubMed
Strogatz, S. H. (2001). Exploring complex networks. Nature, 410(6825), 268.CrossRefGoogle ScholarPubMed
Tagarelli, A., & Interdonato, R. (2013). Who’s out there? Identifying and ranking lurkers in social networks. Proceedings of the 2013 IEEE/ACM international conference on advances in social networks analysis and mining (pp. 215–222). ACM.Google Scholar
Tagarelli, A., & Interdonato, R. (2014). Lurking in social networks: topology-based analysis and ranking methods. Social Network Analysis and Mining, 4(1), 230.CrossRefGoogle Scholar
Tao, Z., Zhongqian, F., & Binghong, W. (2006). Epidemic dynamics on complex networks. Progress in Natural Science, 16(5), 452–457.CrossRefGoogle Scholar
Tsoumakos, D., & Roussopoulos, N. (2006). Analysis and comparison of p2p search methods. Proceedings of the 1st international conference on scalable information systems (p. 25). ACM.Google Scholar
Ushijima-Mwesigwa, H., Khan, M. D., Chowdhury, M. A., & Safro, I. (2017). Optimal installation for electric vehicle wireless charging lanes. arxiv preprint arxiv:1704.01022.Google Scholar
Van Mierlo, T. (2014). The 1% rule in four digital health social networks: An observational study. Journal of Medical Internet Research, 16(2).CrossRefGoogle Scholar
Vilathgamuwa, D. M., & Sampath, J. P. K. (2015). Wireless power transfer for electric vehicles, present and future trends. Plug in electric vehicles in smart grids (pp. 33–60). Springer.Google Scholar
Wang, P., Hunter, T., Bayen, A. M., Schechtner, K., & González, M. C. (2012). Understanding road usage patterns in urban areas. Scientific Reports, 2, 1001.CrossRefGoogle ScholarPubMed
Wang, Y., Yun, X., & Li, Y. (2007). Analyzing the characteristics of gnutella overlays. Fourth international conference on information technology, 2007 (ITNG’07) (pp. 1095–1100). IEEE.Google Scholar
Watts, D. J., Peretti, J., & Frumin, M. (2007). Viral marketing for the real world. Harvard Business School Pub.Google Scholar
Wood, R. K. (1993). Deterministic network interdiction. Mathematical and Computer Modelling, 17(2), 1–18.CrossRefGoogle Scholar
Yan, G., Zhou, T., Hu, B., Fu, Z-Q., & Wang, B-H. (2006). Efficient routing on complex networks. Physical Review E, 73(4), 046108.CrossRefGoogle ScholarPubMed
Zhang, Y., Wang, X., Zeng, P., & Chen, X. (2011). Centrality characteristics of road network patterns of traffic analysis zones. Transportation Research Record: Journal of the Transportation Research Board, 2256(1), 16–24.CrossRefGoogle Scholar
Zhao, L., Xie, W., Gao, H. O., Qiu, X., Wang, X., & Zhang, S. (2013). A rumor spreading model with variable forgetting rate. Physica A: Statistical Mechanics and Its Applications, 392(23), 6146–6154.CrossRefGoogle Scholar