The gap of upper and lower bounds of controlling centrality.

Abstract

<p>(a) HT09 (b) SG-Infectious (c) Fudan WIFI. For the dataset of 'HT09', two temporal networks are generated: i) a temporal network (113 nodes and 9865 interactions) with all nodes and interactions within record of dataset, denoted as 'all range', ii) a temporal network (73 nodes and 3679 interactions) with nodes and interactions after removing the most powerful nodes (nodes with the largest controlling centrality) in the temporal network of i), denoted as 'removed'. For the dataset of 'SG-Infectious', three temporal networks are generated: i) a temporal network (1321 nodes and 20343 interactions) with nodes and interactions recorded in the first week, denoted as 'Week 1', ii) a temporal network (868 nodes and 13401 interactions) with nodes and interactions recorded in the second week, denoted as 'Week 2', iii) a temporal network (2189 nodes and 33744 interactions) with nodes and interactions recorded in the first two weeks, denoted as 'Week 1&2'. For the dataset of 'Fudan WIFI', three temporal networks are generated: i) a temporal network (1120 nodes and 12833 interactions) with nodes and interactions recorded in the first day, denoted as 'Day 1', ii) a temporal network (2250 nodes and 25772 interactions) with nodes and interactions recorded in the second day, denoted as 'Day 2', iii) a temporal network (1838 nodes and 27810 interactions) with nodes and interactions recorded at Access Point No. 713, denoted as '713 point'. The upper and lower bounds of the controlling centrality are given by analytical results in the main text, and the gap is given by the absolute value of the difference of the upper and lower bounds. The aggregated degree of a node is the number of neighbored nodes whom it interacts within the corresponding temporal network. All the gaps are minor when compared with the sizes of these temporal networks.</p

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