Abstract
Recent research has shown the deep impact of the dynamics of human interactions (or temporal social networks) on the spreading of information, opinion formation, etc. In general, the bursty nature of human interactions lowers the interaction between people to the extent that both the speed and reach of information diffusion are diminished. Using a large database of 20 million users of mobile phone calls we show evidence this effect is not homogeneous in the social network but in fact, there is a large correlation between this effect and the social topological structure around a given individual. In particular, we show that social relations of hubs in a network are relatively weaker from the dynamical point than those that are poorer connected in the information diffusion process. Our results show the importance of the temporal patterns of communication when analyzing and modeling dynamical process on social networks.

• Social capacity: the number of relationships humans can maintain opened and which is limited
• Social activity: the number of relationships human form and destroy as a consequence of their daily tasks, family, events, etc.

Social capacity and activity are very heterogenous and while most individuals have small capacity and activity, some might have large values for those characteristics. The ratio between these characteristics of human interaction determines the social strategy:

• Social keepers: these people have a small social activity compared to their social capacity, that is, they interact mostly with the same people in a time interval and form/destroy a small number of ties.
• Social explorers: the opposite strategy, meaning that most of the interactions of these people are form and destroyed rapidly while keeping a very small number of stable connections.
• Social balanced: most of the people have a balance social strategy in which the number of form/destroy interactions is proportional to their capacity.

To show how these strategies look like, we have produce the following videos where you can see the tie dynamics around a social explorer and a social keeper (red nodes) for a period of 7 months. Note that if you aggregate the activity of these two people over those 7 months, the will have the same connectivity. But clearly their instantaneous network is very different!

So, what do you think is your social strategy? Are you a social explorer or a social keeper?

Social explorer

Click here to view the embedded video.

Social keeper

Click here to view the embedded video.

Note: these videos are produced using R and the igraph library. Learn how to make them in my post here

La Caballería andante (…) es una ciencia, dijo Don Quijote (…) que encierra en sí todas o las más ciencias del mundo (…) el que la profesa ha de ser jurisperito, y saber las leyes de la justicia distributiva y conmutativa (…) ha de ser teólogo, para saber dar razón de la cristiana ley que profesa (…); ha de ser médico, principalmente herbolario, parara conocer (…) las yerbas que tienen virtud de sanar las heridas (…); ha de ser astrólogo, para conocer por las estrellas cuántas horas son pasadas la noche (…); ha de saber las matemáticas, porque a cada paso se le ofrecerá tener necesidad de ellas (…).

Knight-errantry (…) is a science, said Don Quixote (…) that comprehends in itself all or most of the sciences of the world, for he who professes it must be a jurist, and must know the rules of justice, distributive and equitable (…) he must be a theologian, so as to be able to give a clear and distinctive reason for the Christian faith he professes (…); must be a physician, and above all a herbalist, so as (…) to know the herbs that have the property of healing wounds (…); he must be an astronomer, so as to know by the stars how many hours of the night have passed (…) He must know mathematics for at every turn some occasion for them will present itself to him (…)

Miguel de Cervantes Saavedra
El Ingenioso Hidalgo Don Quijote de La Mancha
Second part, Chapter XVIII, Madrid 1615

Coco Krumme, Alejandro Llorente, Manuel Cebrian, Alex (“Sandy”) Pentland & Esteban Moro, Sci. Rep. 3, 1645; DOI:10.1038/srep01645 (2013). [link]

Abstract
We consider hundreds of thousands of individual economic transactions to ask: how predictable are consumers in their merchant visitation patterns? Our results suggest that, in the long-run, much of our seemingly elective activity is actually highly predictable. Notwithstanding a wide range of individual preferences, shoppers share regularities in how they visit merchant locations over time. Yet while aggregate behavior is largely predictable, the interleaving of shopping events introduces important stochastic elements at short time scales. These short- and long-scale patterns suggest a theoretical upper bound on predictability, and describe the accuracy of a Markov model in predicting a person’s next location. We incorporate population-level transition probabilities in the predictive models, and find that in many cases these improve accuracy. While our results point to the elusiveness of precise predictions about where a person will go next, they suggest the existence, at large time-scales, of regularities across the population.

Media coverage

• All real-world shoppers are zombies [Lifehacker]
• Animales de costumbres a la hora de la compra [ABC.es]
• Consumers almost always buy in the same shops [UC3M, Eurekalert, Phys.org, ScienceDaily]
• Compramos casi siempre en las mismas tiendas [UC3M, Puromarketing]
• Consument keert altijd terug naar dezelfde winkels [Express.be]
• Shopping Happiness is Bursts of Spontaneity Within The Routine [AnalyzingMedia]
• Shoppers almost always land up at same place to buy [Truthdive]
• Creatures of habit [Beyond Madison Avenue]
• Los hábitos de los consumidores son monótonos y repetitivos [Tendencias21]

Abstract
Social connectivity is the key process that characterizes the structural properties of social networks and in turn processes such as navigation, influence or information diffusion. Since time, attention and cognition are inelastic resources, humans should have a predefined strategy to manage their social interactions over time. However, the limited observational length of existing human interaction datasets, together with the bursty nature of dyadic communications have hampered the observation of tie dynamics in social networks. Here we develop a method for the detection of tie activation/deactivation, and apply it to a large longitudinal, cross-sectional communication dataset (≈19 months, ≈ 20 million people). Contrary to the perception of ever-growing connectivity, we observe that individuals exhibit a finite communication capacity, which limits the number of ties they can maintain active. In particular we find that men have an overall higher communication capacity than women and that this capacity decreases gradually for both sexes over the lifespan of individuals (16-70 years). We are then able to separate communication capacity from communication activity, revealing a diverse range of tie activation patterns, from stable to exploratory. We find that, in simulation, individuals exhibiting exploratory strategies display longer time to receive information spreading in the network those individuals with stable strategies. Our principled method to determine the communication capacity of an individual allows us to quantify how strategies for human interaction shape the dynamical evolution of social networks.

Abstract

The Internet and social media have enabled the mobilization of large crowds to achieve time-critical feats, ranging from mapping crises in real time, to organizing mass rallies, to conducting search-and-rescue operations over large geographies. Despite significant success, selection bias may lead to inflated expectations of the efficacy of social mobilization for these tasks. What are the limits of social mobilization, and how reliable is it in operating at these limits? We build on recent results on the spatiotemporal structure of social and information networks to elucidate the constraints they pose on social mobilization. We use the DARPA Network Challenge as our working scenario, in which social media were used to locate 10 balloons across the United States. We conduct high-resolution simulations for referral-based crowdsourcing and obtain a statistical characterization of the population recruited, geography covered, and time to completion. Our results demonstrate that the outcome is plausible without the presence of mass media but lies at the limit of what time-critical social mobilization can achieve. Success relies critically on highly connected individuals willing to mobilize people in distant locations, overcoming the local trapping of diffusion in highly dense areas. However, even under these highly favorable conditions, the risk of unsuccessful search remains significant. These findings have implications for the design of better incentive schemes for social mobilization. They also call for caution in estimating the reliability of this capability.

Media coverage

• How social media mobilizes society [LiveScience]
• La movilización por redes sociales puede ser rápida, pero tiene límites (EFE, El Diario Vasco, La Información, Muy Interesante) [link,link2]
• Researchers root out the limits of social mobilization [Phys.org]
• Usar las redes sociales para movilizar tiene límites [UC3M, ABC.es, Finanzas.com EFE, AgenciaSinc, Madri+d]
• Using social networks for mobilization has its limits [UC3M, ScienceNewsLine]
• ¿Son las Redes sociales una buena herramienta de movilización social en situaciones críticas ? (audio) [RTVE]
• Las movilizaciones en redes sociales son muy eficientes, si están dirigidas [Tendencias21]
• Facebook passes research test for quick responses, collaboration [NBCNEWS.com]
• Social media has limited mobilisation power [ABC Science]
• Las movilizaciones en las redes sociales son rápidas, pero con un alto riesgo de fracaso [RDI Press]
• Researchers look into the use of social networks in emergency communications [Continuity Central]
• Un experimento pone a prueba a las redes sociales [La Razón]
• Masdar Institute Researchers Quantify the ‘Reliability’ of Social Media for Time-Critical Mobilization [Zawya]
• MI researchers quantify ‘reliability’ of social media for mass mobilisation [The Gulf Today]
• El poder y la flaqueza de las redes sociales [Conec]

To me, the main question when modeling a process in the social sciences is “when does emulation count as explanation?”

— John Myles White (@johnmyleswhite) 25 de marzo de 2013

Interesting question. I guess the problem is that sometimes in science a model does not pretend to make any prediction, neither is supported by any relevant data. It simply emulates reality.

Abstract

We used a large database of 9 billion calls from 20 million mobile users to examine the relationships between aggregated time spent on the phone, personal network size, tiestrength and the way in which users distributed their limited time across their network (disparity). Compared to those with smaller networks, those with large networks did not devote proportionally more time to communication and had on average weaker ties (as measured by time spent communicating). Further, there were not substantially different levels of disparity between individuals, in that mobile users tend to distribute their time very unevenly across their network, with a large proportion of calls going to a small number of individuals. Together, these results suggest that there are time constraints which limit tie strength in large personal networks, and that even high levels of mobile communication do not fundamentally alter the disparity of time allocation across networks.

Abstract

Recent research has focused on the monitoring of global-scale online data for improved detection of epidemics, mood patterns, movements in the stock market, political revolutions, box-office revenues, consumer behaviour and many other important phenomena. However, privacy considerations and the sheer scale of data available online are quickly making global monitoring infeasible, and existing methods do not take full advantage of local network structure to identify key nodes for monitoring.

Here, we develop a model of the contagious spread of information in a global-scale, publicly-articulated social network and show that a simple method can yield not just early detection, but advance warning of contagious outbreaks. In this method, we randomly choose a small fraction of nodes in the network and then we randomly choose a “friend” of each node to include in a group for local monitoring. Using six months of data from most of the full Twittersphere, we show that this friend group is more central in the network and it helps us to detect viral outbreaks of the use of novel hashtags about 7 days earlier than we could with an equal-sized randomly chosen group. Moreover, the method actually works better than expected due to network structure alone because highly central actors are both more active and exhibit increased diversity in the information they transmit to others. These results suggest that local monitoring is not just more efficient, it is more effective, and it is possible that other contagious processes in global-scale networks may be similarly monitored.

1. generate a number of snapshots of the network at different times using R and igraph, and
2. then put them together in a video file using ffmpeg.

For 1. we need to draw the temporal network at each snapshot. Given the set of nodes and edges present at a given time, we have to find a layout for that instantaneous graph. The layout is a two-dimensional visualization of the nodes and edges in the plane and there are many algorithms to produce it. The package igraph contains mainly Force based algorithms like for example the Kamada-Kawai or Fruchterman-Reingold ones. Your millage may vary from one algorithm to another since visualizations depend on the number of nodes, clustering and/or community structure of the network. Sounds easy, but there two big problems with this approach:

• Force based layout algorithms consist on performing a number of iterations aimed to minimize the energy of physical forces between nodes, and starting from an initial configuration which is typically a random initial condition. This means that even if your network does not evolve in time, successive calls to the layout algorithm will produce different results. In our temporal network case it means that the layout from one snapshot to the next one will be very different producing a swarm-of-bees kind of motion. For example, if you run this script you will see that the four layouts are very different:

  library(igraph)
  par(mfrow=c(2,2),mar=c(0,0,0,0), oma=c(0,0,0,0))
  g <- watts.strogatz.game(1,20,3,0.4)
  for(i in 1:4) plot(g,layout=layout.fruchterman.reingold,margin=0)
  

  Luckily, in igraph 0.6 we can specify the initial position of the nodes for some layout functions: layout.graphopt, layout.kamada.kawai and layout.fruchterman.reingold. My personal experience is that layout.graphopt crashes in this 0.6 version (although it works on 0.5), so we are left with the other two algorithms. The plan (taken from this original idea of Tamás Nepusz, one of the developers of igraph) is to use the layout of the previous snapshot as the initial condition for the next snapshot layout so we have a smooth transtion from one to the other. In the example above, the implementation will be the following using the start parameter:

  library(igraph)
  par(mfrow=c(2,2),mar=c(0,0,0,0), oma=c(0,0,0,0))
  g <- watts.strogatz.game(1,20,3,0.4)
  layout.old <- layout.fruchterman.reingold(g)
  for(i in 1:4){
       layout.new <- layout.fruchterman.reingold(g,params=list(niter=10,maxdelta=2,start=layout.old))
       plot(g,layout=layout.new)
       layout.old <- layout.new
       }
  

  Now you can see that the layouts are similar. There are two new parameters passed to the layout function: niter = 10 specify the number of iterations (10) of the minimization of energy procedure in the force based algorithm. This number should be small, otherwise the final result will be very different from the initial condition. The same happens for the other parameter maxdelta=2 which controls the maximum change in the position of the nodes allowed in the minimization procedure.

• The other problem is that in a temporal network nodes and/or edges appear and disappear dynamically. Thus the time dependent graph might have different number of nodes and/or edges from one snapshot to the next one. This means that the layout at a given snapshot cannot be used as the initial condition to generate next time layout, since the number of nodes can be different. My solution to this problem is to consider all (past/present/future) nodes/edges when calculating the layout but to display only present nodes/edges in the plot by making past and future nodes/edges transparent. This trick allows the reutilization of the layouts between steps, but it will produce a more or less steady visualization in which the layout at any given time is not related to the instantaneous structure of the temporal graph. To overcome this problem we take advantage of another property of force based algorithms: nodes which are connected attract each other along the edge. At a given instant, we could then modify the attraction between nodes along edges depending on whether the the edge is not present. In igraph 0.6, only the layout.fruchterman.reingold has this possibility through the parameter weights, a vector giving edge weights which are use to multiply the attraction along the edge. For example we could set weight equal to one if the edge is present and use zero weight for the rest. This will produce a layout in which present nodes are tightly connected while the past/future nodes are repelled from them. This effect dramatically highlights the appearance and disappearance of nodes, but could create too much confusion if there are many of those events.

To test this ideas, we will work an important example in the theory of complex networks: the preferential attachment mechanism to generate scale-free networks, i.e. the Barabási-Albert model. In our implementation, we keep the mechanism very simple: starting from an initial core of nodes, at each time step we add a single node that connects to m existing nodes which are selected proportionally to the number of links that the existing nodes already have. This mechanism leads to heavily linked nodes ("hubs") together with a large fraction of poorly connected nodes. A particular realization of this model can be found in the file edges.csv below. The structure of the file is simple each line of the form id1 | id2 | time indicates that a link between id1 and id2 appears at a particular time. Depending on the context this might represent that the tie was activated at that particular instant (for example if it is a RT between two twitter accounts) or that it was the time in which the edge appeared first (like in our Barabási-Albert model). Here is the code to generate the snapshots and producing a PNG picture for each of them: As you can see the edges present before time ti are colored in "gray" and weighted 1 while the rest are transparent rgb(0,0,0,0) and weighted 0. For the nodes we have used the function graph.strength that calculate the sum of weights of adjacent edges of a node: note that if at a given instant a node has no active adjacent edges, its graph strength is zero and thus the node is transparent. Otherwise it is colored as in the vcolor vector. Final step is to encode this images into a video format. To that end I have used ffmpeg which can be install in linux, windows or mac. The following command line in a terminal shell produces a video file output.mp4 in the mpeg format:

ffmpeg -r 10 -b 20M -i example%03d.png output.mp4

The first -r 10 flag controls the rate of frames per second (fps), 10 in this case, while the -b 20M sets the bitrate in the output (set to a large value here, 20M). The result is the following video

Click here to view the embedded video.