Using core-periphery structure to predict high centrality nodes in time-varying networks

Abstract

Vertices with high betweenness and closeness centrality represent influential entities in a network. An important problem for time varying networks is to know a-priori, using minimal computation, whether the influential vertices of the current time step will retain their high centrality, in the future time steps, as the network evolves. In this paper, based on empirical evidences from several large real world time varying networks, we discover a certain class of networks where the highly central vertices are part of the innermost core of the network and this property is maintained over time. As a key contribution of this work, we propose novel heuristics to identify these networks in an optimal fashion and also develop a two-step algorithm for predicting high centrality vertices. Consequently, we show for the first time that for such networks, expensive shortest path computations in each time step as the network changes can be completely avoided; instead we can use time series models (e.g., ARIMA as used here) to predict the overlap between the high centrality vertices in the current time step to the ones in the future time steps. Moreover, once the new network is available in time, we can find the high centrality vertices in the top core simply based on their high degree. To measure the effectiveness of our framework, we perform prediction task on a large set of diverse time-varying networks. We obtain F1-scores as high as 0.81 and 0.72 in predicting the top m closeness and betweenness centrality vertices respectively for real networks where the highly central vertices mostly reside in the innermost core. For synthetic networks that conform to this property we achieve F1-scores of 0.94 and 0.92 for closeness and betweenness respectively. We validate our results by showing that the practical effects of our predicted vertices match the effects of the actual high centrality vertices. Finally, we also provide a formal sketch demonstrating why our method works.

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Notes

  1. 1.

    In this paper, when we mention highly central vertices, we specifically refer to high closeness or betweenness centrality and not other types of centralities.

  2. 2.

    We tried with other stretches of size 15, 25 etc. The results do not seem to be affected by such minor variations. Ideally this size should not be too large thus consuming a lot of data for prediction, nor it should be too small thus having too few points to correctly predict. Through experimentation, we find that a size close to 20 strikes an ideal balance.

  3. 3.

    Note that if we keep increasing the number of top vertices, the prediction results can only get better. Through experiments, we observe that small numbers like 5 and 10 are judicial choices.

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Correspondence to Soumya Sarkar.

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Sarkar, S., Sikdar, S., Bhowmick, S. et al. Using core-periphery structure to predict high centrality nodes in time-varying networks. Data Min Knowl Disc 32, 1368–1396 (2018). https://doi.org/10.1007/s10618-018-0574-x

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Keywords

  • Network analysis
  • Prediction
  • Centrality
  • Temporal and time series data
  • Core periphery