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Mathematical Underpinnings of AnalyticsTheory and Applications$
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Peter Grindrod

Print publication date: 2014

Print ISBN-13: 9780198725091

Published to Oxford Scholarship Online: March 2015

DOI: 10.1093/acprof:oso/9780198725091.001.0001

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Dynamically evolving networks

Dynamically evolving networks

Chapter:
(p.57) 2 Dynamically evolving networks
Source:
Mathematical Underpinnings of Analytics
Author(s):

Peter Grindrod CBE

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198725091.003.0003

This chapter considers centrality measures for static and evolving networks of various different types. In particular it considers networks that evolve both discretely and continuously in time. In each case it shows how the notion of centrality may be extended to such situations so as to identify influential broadcasters and listeners. The chapter considers how this might relate to the fragility of networks and to problems of discounting old information and updating in real time. This exploits matrix algebra and matrix valued functions. Presented are examples of mobile phone social networks and corporate email networks.

Keywords:   Katz centrality, matrix valued functions, corporate email networks, mobile phone call networks, network fragility, discrete time evolving networks, continuous time evolving networks

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