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Limited communication capacity unveils strategies for human interaction

Giovanna Miritello, Rubén Lara, Manuel Cebrián, Esteban Moro

arXiv:1304.1979v1physics.soc-phcs.SI

TL;DR

Existing datasets have limited duration and bursty communications, hindering observation of tie activation and deactivation. The paper analyzes longitudinal mobile-phone records with a method that separates communication capacity from activity. It finds diverse social strategies, and simulations show that exploratory strategies are associated with longer information-reception times than stable strategies.

  • Problem

    Limited observation periods and bursty communications hinder large-scale measurement of tie activation and deactivation dynamics.

  • Method

    The paper analyzes 19 months of reciprocated mobile-phone communication records from about 20 million users and separates communication capacity from tie-formation activity.

  • Results

    Exploratory strategies are associated with longer information-reception times, while weak ties are mostly associated with social explorers and short-lived communications.

  • Takeaways & Limitations

    Stable and exploratory strategies shape network properties including tie persistence, structural diversity, and information diffusion beyond total connectivity alone.

  • Takeaways & Limitations

    The observational methodology and period cannot establish causality between social strategies and homophily in static network properties.

Abstract

from arXiv · show

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 ($\approx$ 19 months, $\approx$ 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.

1. Detection of tie activation/deactivation

The paper detects tie activation and deactivation by combining activity inside a 7-month observation window with activity before and after it, using longitudinal mobile-phone records.

  • 19 months of anonymized voice-call records cover about 20 million users and 700 million communication ties.
  • The analysis retains users active throughout the period and only reciprocated ties after filtering calls involving other operators.
  • Only 3.5% of links have an inter-event time longer than the relevant observation interval, supporting the activation/deactivation definition.

2. Communication capacity and activity

The paper separates active-tie capacity from tie-formation activity and finds that people continually renew ties while keeping their active social capacity nearly stable over the observation window.

  • Communication capacity and activity: nα,i(T) ≃ nω,i(T) for most users, so activated and deactivated ties nearly balance over T = 7 months.
  • Communication capacity and activity: Around 90% of users show approximately linear tie activation and deactivation, with αi ≃ ωi and nearly constant communication capacity κi(t).
  • Communication capacity and activity: Average social persistence is around 75%, compared with 50% in a model where all ties have equal activation and deactivation probabilities.
  • Communication capacity and activity: Communication capacity κi measures currently managed relationships, whereas activity nα,i or αi measures relationships established and their rate.
  • Communication capacity and activity: Social-circle size, communication capacity, and activity decrease gradually with age, while women maintain smaller social circles than men on average.

3. Social strategy

The paper defines social strategy as the balance between communication activity and capacity, distinguishing stable social keepers from exploratory social explorers. These strategies correspond to different network structures and information-access times.

  • Social strategy: Social strategy γ_i = nα,i/κ_i compares tie activation activity with communication capacity.Values near β represent balanced behavior; γ_i ≪ β identifies social keeping, whereas γ_i ≫ β identifies social exploring.
  • Social strategy: Figure 4 shows individual neighborhoods over time and the population-level relation between activity and capacity.The plotted reference is nα,i = 0.75κ_i, with iso-connectivity curves for k_i = 10, 20, and 50.
  • Relation to topological properties: Social keepers retain 90% of initial ties, compared with 52% for social explorers, while clustering for fixed k_i is twice as high among keepers.Social strategies are also assortative, with Pearson coefficient ρ(γ_i,γ_nn,i) ∼ 0.3.
  • Information diffusion: Controlling for connectivity and communication events, social explorers receive spreading information roughly 2–3 days later than social keepers.The result comes from Susceptible-Infected simulations run on the observed sequence of communication records.
  • Information diffusion: For γ > β, the number of individuals with high communication strength decreases exponentially, and highly exploratory individuals experience very long information-access times.The passage attributes this pattern to high activity combined with short tie lifetimes.

4. Discussion

The discussion relates exploratory and stable strategies to weak ties, demographic patterns, and network structure. It also emphasizes that the observational methodology cannot establish causality.

  • 4. Discussion: Figure 5 compares average capacity and activity across age and gender groups, using overall averages and the PCA relation nα,i = βκ_i as references.The discussion reports that women maintain smaller social circles than men, with age-related changes in both capacity and activity.
  • 4. Discussion: Weak ties are disproportionately generated by social explorers and are usually activated and deactivated within a short time span.The average tie weight is negatively correlated with social strategy, ρ(logγ_i,logw_ij) ≃ −0.32 ± 0.01.
  • 4. Discussion: Only almost 20% of ties with fewer than 10 calls remain active throughout the observation window.Such ties represent 50% of the whole population of ties in the reported dataset.
  • 4. Discussion: The study cannot establish whether social strategies cause the observed homophily in static network properties.This limitation follows from the methodology and observational period.
  • 4. Discussion: For nearly any connectivity k_i, individuals can exhibit either exploratory strategies with greater structural diversity or stable strategies focused on a conservative neighborhood.Thus, strategy differences occur across multiple connectivity scales and affect resulting network properties.

tinf (days)

Figure 6 relates infection time to social strategy across connectivity groups and, for k_i = 20, to exchanged calls and strategy.

  • tinf (days): Figure 6A plots average infection time against γ_i for connectivity groups k_i = 10, 20, and 50.The Pearson coefficient between t_inf and log(γ_i) is 0.13, with confidence range [0.12,0.14].
  • tinf (days): Figure 6B shows average infection time as a function of exchanged calls w_i and social strategy γ_i for k_i = 20.The panel isolates variation in communication volume and strategy within one connectivity group.
  • tinf (days): The figure supports comparison of infection-time patterns across strategy values while holding the stated connectivity group fixed.For panel B, the fixed group is k_i = 20.

A. Preparing and Sampling the Data

The study constructs a longitudinal communication network from anonymized voice-call records, partitions the observation period, and filters users and ties to reduce sampling artifacts.

  • A. Preparing and Sampling the Data: The dataset contains anonymized voice-call records from one mobile operator in one country, excluding messages and cross-operator calls.The analysis uses voice calls only and cannot recover users’ personal information.
  • A. Preparing and Sampling the Data: The 19-month period is divided into three subintervals to separate tie creation and removal from call activity.The resulting observation window contains 16×10^6 individuals and 130×10^6 ties.
  • A. Preparing and Sampling the Data: Subscription and churn filters remove about 17% of nodes and 37% of reciprocated links within the observation window.These filters are intended to prevent spurious apparent growth or dissolution near the window boundaries.
  • A. Preparing and Sampling the Data: For demographic analyses, users are retained only when their recorded age is between 16 and 70 years.Age and gender information is available for a randomly chosen 40% of users; this filtering removes 0.5% of users with demographic data.

B. Entanglement between bursty activity and tie dynamics

Bursty, heterogeneous communication makes observed connectivity and tie persistence strongly dependent on the observation window. The paper addresses this by distinguishing open from observed ties and modeling waiting-time effects before detecting formation and decay.

  • Bursty activity: Heavy-tailed inter-event times make short observation windows miss ties, while longer windows are needed to assess whether ties formed or decayed.The database reports an average inter-event time of 14 days and standard deviation of 18 days; 3% of ties showed no activity within the observation window.
  • Empirical diagnostics: A universal rescaled inter-event-time distribution is reported across ties, while persistence depends on whether ties are required to show activity at the sampled week.Figure 7 contrasts activity-based persistence with persistence of open ties.
  • Tie detection: The method uses activity six months before and after the observation window to classify ties as old or persistent, reducing spurious formation and decay assignments.A tie observed before the window is treated as old, while activity after the window indicates persistence.
  • Apparent connectivity growth: Observed connectivity can grow as ki(t) ∼t^γ even when all links remain open, because bursty and heterogeneous activity delays first observations.For short times, the apparent growth can have γ ≃ 1/2 and resemble network-growth models.
  • Tie activation and deactivation: Most people form and remove edges at nearly constant rates, but the time gaps between these events are non-Poissonian and exhibit short-time burstiness.The distributions for different activity-rate groups collapse onto a common curve, suggesting a universal bursty form.

E. Statistical evidence for the conservation of social capacity

The study tests whether tie activation and deactivation balance at the individual level. Observed rates agree well with a matched Poisson null model, supporting approximately conserved social capacity while leaving a small set of outliers unexplained.

  • Rate balance: For a given individual, the tie-formation rate αi approximately equals the tie-decay rate ωi, implying a roughly constant number of open connections.The paper interprets this balance as conservation of social capacity.
  • Null model: A Poisson null model uses separate formation and decay processes with equal rates, while incorporating each user’s observed activity heterogeneity.The model sets λi = nω,i/212 per day for both processes.
  • Statistical evidence: The observed counts nα,i(T) and nω,i(T), and the measured αi and ωi, agree well with simulations from the matched null model.The agreement is reported at the observation-window time scale and for the estimated rates.
  • Residual deviations: A small amount of outliers cannot be explained by the null model.This bounds the conservation result as an approximate population-level pattern rather than a complete account of every individual.

F. Measuring neighborhood persistence

Measured neighborhood persistence is 75%, compared with 50% under randomized neighbor replacement, indicating that people renew social ties non-randomly and relatively slowly.

  • 75% average persistence means users retain three-quarters of their initial neighbors after the observation period.The persistence measure is the fraction of neighbors present at the beginning and still active at the end.
  • 50% randomized persistence contrasts with 75% in the measured network, showing that tie activation and deactivation are not random.The random model preserves users’ strategies and event times but randomizes which neighbors are added or removed.
  • Users therefore renew their social circles slowly, while some ties are more likely to be destroyed than others.

G. Relation of the social strategy with topological properties

Social strategy is associated with tie persistence, clustering, and assortative organization: keepers maintain stable, clustered neighborhoods, whereas explorers have more volatile neighborhoods.

  • Social keepers with γ < 0.2 retain up to 90% of initial ties, whereas social explorers with γ > 2 retain as little as 40% after seven months.
  • Aggregated clustering reaches 0.22 for social keepers but decreases to 0.05 for social explorers.Clustering also decreases with increasing connectivity, so connectivity and strategy jointly shape neighborhood structure.
  • Clustering can be similar for highly connected keepers and less connected explorers because connectivity and strategy have opposing effects.
  • Social strategies are assortative, with keepers interacting more often with keepers and explorers with explorers.This produces relatively static keeper zones and highly volatile explorer clusters across the global network.

H. Facebook data set

Facebook data provide a lower-activity comparison in which users still conserve communication capacity and show the same assortative separation of social strategies observed in mobile-phone data.

  • Facebook users averaged 3.01 formed and 3.02 decayed ties over seven months, indicating approximately balanced social activity.The filtered dataset contained users active before and after the observation window, without requiring reciprocated links.
  • Facebook users with more than 10 events conserved open connections, with average capacity ⟨κ_i(t)⟩ = 3.23.For these users, nα,i(T) ≃ nω,i(T) and α_i ≃ ω_i.
  • 81% of activity variance was explained by nα,i = 1.04κ_i, linking formed ties to communication capacity.
  • Social strategy assortativity in Facebook matched the mobile-phone pattern, with keepers and explorers tending to cluster separately.
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