Applying the mathematics of evolving networks for more effective social media marketing
Submitting InstitutionUniversity of Reading
Unit of AssessmentMathematical Sciences
Summary Impact TypeTechnological
Research Subject Area(s)
Information and Computing Sciences: Computation Theory and Mathematics, Information Systems
Summary of the impact
Researchers in the Centre for the Mathematics of Human Behaviour at the
University of Reading have developed a novel approach for the real-time
monitoring of evolving social networks. These networks, in which
connections between individuals change over time, are an important
opportunity for online advertising. The research has been used in
collaboration with Bloom Media Ltd to develop a new tool that gives their
clients a better understanding of the impacts of social media campaigns.
As a result Bloom are leading the field in this area, allowing them to
attract major new clients and leading to significant growth of the
business. The company now directly employs highly skilled mathematics
graduates specifically to work in this area.
Digital communications between individuals have resulted in large,
multi-layered social networks that evolve from moment to moment. Although
methods exist for analysing and modelling static networks, recent trends
in communications, transport and energy have highlighted the need for
methods that are appropriate for dynamic, evolving networks. Therefore,
funded by an EPSRC Digital Economy programme through the Horizon hub,
Professor Peter Grindrod collaborated with Prof Desmond Higham (University
of Strathclyde) to develop a simple mathematical model of evolving
networks , defined here as a fixed set of vertices (e.g. a group of
people) with edges (e.g. peer-to-peer communication) that appear and
disappear over time. The approach uses a temporal series of snapshot
graphs instead of collapsing different time points on to one (denser)
graph, thereby retaining both information about time-flow and the benefits
of more sparse graphs.
The core of this work involved exploring centrality measures in evolving
networks. Centrality is the relative importance of an individual (a
vertex) and determines its involvement in a network. Prior to this work,
centrality measures had been developed for static networks, but had not
been successfully translated to evolving networks. The full technical
details are given in  although the discussions leading to the impact
were prompted by a SIAM news article , which was written for a wider
Katz centrality computes the relative influence of a node within a static
network by measuring its number of immediate neighbours and other nodes
that connect to it through those immediate neighbours. An attenuation
factor lessens the influence of longer pathways. The researchers built an
extension of Katz centrality for evolving networks that gives
communicability across time steps. When peer-to-peer communications can be
observed, this allows the identification of individual strong broadcasters
and listeners . It can also be scaled up to very large data sets as it
involves handling large but sparse matrices.
Fast algorithmic computations of centrality ranking can be achieved using
sparsity and series approximation. Although for some real applications the
choice of the attenuation factor can be challenging, the researchers
showed that this can be solved simply by normalisation and probabilistic
interpretation of the attenuation factor as a proxy for radius of
The researchers are now working on a continuous version in which edges are
created and destroyed continuously rather than being simply snapshots in
time. Additionally, `memory' is being incorporated into the centrality
ranking, so that recently appearing edges are given more weight than older
Peter Grindrod (Professor, 2008-Sept 2103)
Mark Parsons (PhD student 2010-July 2013; PDRA July-Oct 2013)
Danica Greetham (PDRA Nov 2010-Oct 2011; Lecturer Oct 2011-present)
References to the research
All references are peer-reviewed. , and  are published in highly
regarded international journals,  has since been cited in several
reviews and research articles on temporal networks.  appeared in SIAM
review with 5-year impact factor of 8.  is in SIAM news, which
addresses a wide audience and is a news-journal for world-wide applied
 Grindrod, P., & Higham, D. (2010). Dynamical models, inverse
problems and propagation. Proceedings of the Royal Society, Series A,
vol. 466 no. 2115, 753-770. doi:10.1098/rspa.2009.0456
Citations on Web of Science: 12 as of 18 Sep 2013
 Grindrod, P., Parsons, M. C., Higham, D. & Estrada, E. (2011).
Communicability across evolving networks. Physical Review E, 83,
Issue 4 pp 046120. doi: 10.1103/PhysRevE.83.046120
Citations on Google Scholar: 41 as of 18 Sep 2013
 Desmond J. Higham, Peter Grindrod, and Ernesto Estrada (2011) People
who read this article also read... Part I and II(SIAM) Newsletter article,
SIAM News, Volume 44 , Numbers 1 and 2
 Grindrod, P., & Higham, D. (2011). Models for evolving networks:
with applications in telecommunication and online activities. IMA Journal
of Management Mathematics doi: 10.1093/imaman/dpr001
 Vukadinovic-Greetham, D., Stoyanov, Z., & Grindrod, P. (2013).
Centrality and spectral radius in dynamic networks. Computing and
Combinatorics, Lecture Notes in Computer Science. 7936, pp. 791-800.
Hangzhou, China: Springer. DOI 10.1007/978-3-642-38768-5_72
 Grindrod, P., & Higham, D. (2013). A matrix iteration for
summarizing dynamic networks. SIAM review, 55, 118-128. http://dx.doi.org/10.1137/110855715
1 citation on 18 Sep 2013
Relevant grant funding:
EPSRC grant EP/G065802/1 (as part of `The Horizon Hub' led by the
University of Nottingham)
PI (Reading): Peter Grindrod
Value to Reading £886,658. Period: 01/10/2009 to 31/05/2015.
EPSRC MOLTEN EP/I016031/1
PIs: Peter Grindrod and Desmond Higham (University of Strathclyde)
Title: Mathematics Of Large Technological Evolving Networks.
Value: £171,474. Period: 01/03/2011 to 28/02/2013
TSB #710104 (Awarded to Bloom Media)
PI: Peter Grindrod
Title: Digital Business Analytics for decision makers
Value: £94,000 Period: 01/12/2011 to 30/11/2012
Centre for Defence Enterprise (a part of Defence Science and Technology)
(Awarded to CountingLab Ltd - spin out company of the University of
PI: Peter Grindrod
Title: Applying New Thinking To Counter-Terrorism: Communicability across
an Evolving Social
Network - Determining the biggest influencers, risers and fallers
Value: £40,500 + VAT Period: 01/09/2011 to 12/03/2012
Details of the impact
The research was used in collaboration with digital media agency Bloom
Media Ltd. to develop Whisper, a new data analytics tool capable of
analysing social network data in real time as a framework for return on
investment (RoI) measurement.
Applying the research
In 2011Bloom were looking to speed up the market research cycle and
measure return on investment (RoI) for their clients, something not then
possible for social media campaigns. Bloom's Head of Data Insight, Mr
Peter Laflin, approached Prof Grindrod to discuss a collaborative approach
for commercial development of the research  (which he had read about in
, Section 3).
Initially, the researchers assisted Bloom to secure funding through the
Technology Strategy Board to develop a proof of concept that
communicability could be used to effectively measure social media
marketing campaigns. Ultimately this led to the creation of Whisper ,
described as a world class platform for analysing Twitter and other social
media data feeds and which incorporates algorithms generated by the
research within its engine.
Whisper is marketed by Bloom  as an entirely new planning tool that
allows their clients to monitor the opinions, stories, emotions and
affinities of social media communities discussing topics that resonate
with their clients' products or values. This is achieved using algorithms
developed by the researchers that enable visualisation of the structures
of these communities as they adapt in real time. This enables Bloom to
assess huge data sets and identify the key influencers within these
communities and allows Bloom's clients to engage efficiently with these
communities in real time, giving them insight into their customers' brand
affinity, mood, device use and location.
In a letter to Prof Grindrod , Mr Laflin describes the key role of the
research: "Whisper is the world's first data analytics tool that can
accurately measure the impact and RoI from social media. At the heart of
Whisper is a specific implementation of your work and the measure of
`influence' is a proxy for your communicability ideas". Mr Laflin
highlighted that by the end of 2013, Bloom will have invested over £200k
in this work, and intend to continue investment and development in order
to stay "at the cutting edge of the scientific measurement of marketing".
Impacts within Bloom
The unique insight provided by Whisper has enabled Bloom to alter their
brand direction. As a result of exhibiting the technology, they have
developed substantial new business opportunities, including significant
growth and a range of new clients such as Anglian Home Improvements, ADT
and LA Fitness. Income has doubled to £2.4m and staff numbers have
doubled to 60 during the financial year 2012-2013. Additionally, Bloom
now employs highly skilled mathematics graduates and postgraduates to
develop and grow this increasingly important area. The company have also
developed additional market opportunities by providing analytics services
to other marketing agencies for use under their own names.
This work has significantly raised the profile of the company within the
industry. For example, they have been nominated for the 2013 DADI awards
and the Innovation category of the 2012 Some Comms Awards for their use of
Whisper with Anglian Home Improvements .
Impacts on Bloom's clients
A key aim for Bloom was to provide their clients with clear evidence of
RoI for social marketing activities. The tool and framework have enabled
Bloom to identify the true influencers within a social network, and then
use this information to plan viral content for their clients. This has
enabled Bloom's clients to gain greater value from their marketing
activities and an improved understanding of their customers, leading to
better targeting and changes in their digital marketing approach.
Raising public awareness
Graphics produced by Whisper, which show the evolving networks in a clear
and simple format and demonstrate how network members interact and the
relative influence of individuals, have contributed to the public
understanding of social network interactions. An example was on show at
the Royal Society 2013 Summer Science Exhibition and was runner up in the
Infographics category of the Exhibition's image competition . The
exhibition attracted over 10,000 members of the public including 2,000
school students, with many more reached through coverage on TV, in the
media and online.
The benefits of the research within social media were immediately
recognised, as the methods work efficiently and for large matrices.
However, applications for other sectors are also being developed by the
researchers, and early work with the defence sector has led to a 2011 TSB
grant to develop a proof of concept.
Sources to corroborate the impact
- Whisper: http://www.bloomagency.co.uk/whisper/
- The collaboration between the researchers and Bloom Media was
highlighted in an online article: http://www.thedrum.co.uk/news/2012/03/27/centre-mathematics-human-behaviour-university-reading-appoints-bloom-develop-next
- The impact of the collaboration with Bloom has been highlighted on
their website: http://www.bloomagency.co.uk/measuring-influence-at-digital-futures-2012/
- The collaborative work has also been presented as a conference paper
at SocInfo2012, 5-7 Dec 2012, Lausanne. Laflin P, et al. Dynamic
targeting in an online social medium.
- Letter from Head of Data Insight, Bloom Agency - available upon
- Royal Society Picturing Science 2013 image competition (http://royalsociety.org/grants/picturing-science/).
Runner-up: Infographics category. Image title "Twitter activity: a
snapshot of tweeter-follower interactions as a conversation grows" (http://www.bloomagency.co.uk/from-data-to-art-bloom-at-the-royal-society/;
image at http://www.flickr.com/photos/royalsociety/8691325239/in/set-72157633103539082/lightbox/).
to select outstanding images of science provided by Research Fellows.
The judging criteria are visual impact of the image; public appeal of
the image; and scientific story behind the image.
- Press releases from Bloom http://www.bloomagency.co.uk/adt-helps-keep-home-safe-while-youre-away/
- Figures found at the top of this page http://royalsociety.org/summer-science/proposals/
- Press release from Very - http://www.bloomagency.co.uk/very-and-bloom-team-up-to-push-second-screening-boundaries/