Temporal Networks


 With the increasing uptake of social networks, modelling and analysis of dynamical process on networks becomes relevant in several application areas: well-being, marketing, information retrieval, epidemiology, defense and so on.

Observing and measuring behaviour together with communications through a social network is the first step toward disentangling influence (or contagion) and selection (who is communicating with whom) process on the network.

Several challenges arise in temporal (aka dynamic or evolving) networks with dynamical processes on them: Community detection, centrality ranking of vertices and edges, computational complexity of algorithms that measure some of the networks or processes properties.

Our research in this are includes the following research topics:

Spread of mood in social networks

Large online studies

In this one year project funded by Centre for Defence studies, the main aims were to investigate how moods spreads through large networks and to build a model of collective sentiment dynamics.

We analysed a large sample of UK Twitter users over several months and focused only on their tweets that contained mentions. We found [1] that users with the largest potential communication reach use positive sentiment more often and more strongly than the average user (for similar observations from small face to face studies see below).

Following Twitter communities that form around topics or friendships over a period of months, we found that their sentiment levels are relatively stable. Sudden changes in sentiment from one day to the next can be traced to external events affecting the community. We then created a simple agent-based model capable of reproducing measures of emotive response comparable to those observed.

Small human studies

In this one year research project funded by Unilever, the aim was to incorporate social psychological theories in the building of mathematical models of the spread of mood through networks. We also wanted to explore different strategies for behaviour change interventions using small scale experimental studies.

Together with Dr Robert Hurling, behaviour change expert from Unilever R&D in Colworth we investigated temporal networks coupled with attitudes/behaviours. Our goal was to identify what is dynamics of positive and negative affect (independent constructs that are often used to describe ephemeral mood) in an evolving social network. We also looked at the optimal choice of nodes/individuals who should be triggered in order for behaviours to evolve in wanted directions.

In these projects we have conducted

- Analysis of centrality in dynamic networks

- Research on how to disentangle selection and influence processes on networks

- Analysis of different strategies when choosing "the agents of change" for a behaviour change intervention.

Our results [2,7] have shown that positive and negative affect are independent and not complementary and that they follow different dynamics in small social networks. while positive affect goes toward a mean, negative affect tends to go toward observed extremes in a social network. We were able to find evidence of both positive and negative affect contagion in small human networks. Using gratitude exercises to improve positive and reduce negative affects, we have shown that the blanket intervention works well, but a selective intervention can have qualitatively different results based on the selection process. Finally we observed that the individuals with the least negative affects levels at the beginning of the study were the best "broadcasters" - having the largest potential reach.  


  •  Positive Affect  Negative Affect

 Modelling of conversations on Twitter

In order to explore mechanisms of online conversations, we looked at the underlying structure and timings of two large temporal networks based on two large UK twitter datasets, one of around four million tweets collected between December 2011 and January 2012 over 28 days [4,5] and the other of around 120 million tweets collected over 2014 to 2015. We proposed a simple method of identifying conversations between pairs of users, based on a time-threshold on the time-to-next tweet, and found evidence that a threshold of nine hours gives a good indication of distinct conversations.

To model burstiness of Twitter conversations (where messages between individuals are not exchanged in regular time intervals but irregular periods of high activity followed by long periods of inactivity) we used a modified Bernoulli process.

We consider a dynamics network where each individual forms and breaks connections according to this process. The value of messaging probability x in time t for each individual depends on the fitness distribution from which it is drawn. We added a memory effect, where the event probability is increased proportionally to the number of events which occurred within a given amount of time preceding t.

We have shown that for small values of x the inter-event time distribution follows a power-law. We also found exact solutions for the expectation of the degree distribution for a variety of possible fitness distributions, where the memory effect either is, or is not present. Based on these results, we hope to develop methods to uncover hidden fitness distributions from fast changing, temporal network data such as online social communications and networks obtained from neuroimaging.



To access publication click on link below or to access all publications see right hand box:

[1] Charlton, N., Singleton, C. and Vukadinovic Greetham, D. (2016) In the mood: the dynamics of collective sentiments on Twitter. Royal Society Open Science. doi: 10.1098/rsos.160162 (In Press)

[2] Vukadinovic Greetham, D., Sengupta, A., Hurling , R. and Wilkinson , J. (2015) Interventions in social networks: impact on mood and network dynamics. Advances in Complex Systems, 18 (03n04). p. 1550016. ISSN 1793-6802 doi: 10.1142/S0219525915500162

[3] Colman, E. and Vukadinovic Greetham, D. (2015) Memory and burstiness in dynamic networks. Physical Review E, 92 (1). 012817. ISSN 1539-3755 doi: 10.1103/PhysRevE.92.012817

Vukadinovic Greetham, D., Stoyanov, Z. and Grindrod, P. (2014) On the radius of centrality in evolving communication networks. Journal of Combinatorial Optimization, 28 (3). pp. 540-560. ISSN 1382-6905 doi: 10.1007/s10878-014-9726-0

[4] Vukadinovic Greetham, D., Poghosyan, A. and Charlton, N. (2014) Weighted alpha-rate dominating sets in social networks. In: Third International Workshop on Complex Networks and their Applications , 23-27 Nov 2014, Marrakech, Morocco. (In Press)

[5] Vukadinovic Greetham, D. and Ward, J. A. (2014) Conversations on Twitter: structure, pace, balance. In: 2nd International Workshop on Dynamic Networks and Knowledge Discovery (DyNaK II), 15 September 2014, Nancy, France. (ISSN 1613-0073)

[6] Smith, G., Stoyanov, Z., Vukadinovic Greetham, D., Grindrod, P. and Saddy, D. (2014) Towards the computer-aided diagnosis of dementia based on the geometric and network connectivity of structural MRI data. In: CADDementia workshop, Medical Image Computing and Computer Assisted Intervention (MICCAI) 2014 conference, 14-18 Sep 2014, Boston.

[7 ]Vukadinovic Greetham, D., Hurling, R., Osborne, G. and Linley, A. (2011) Social networks and positive and negative affect. Procedia Social and Behavioural Sciences, 22. pp. 4-13. ISSN 1877-0428 doi: 10.1016/j.sbspro.2011.07.051


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