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Link to original content: https://pubmed.ncbi.nlm.nih.gov/21826200
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. 2011;6(8):e22656.
doi: 10.1371/journal.pone.0022656. Epub 2011 Aug 3.

Modeling users' activity on twitter networks: validation of Dunbar's number

Bruno Gonçalves  1 , Nicola Perra, Alessandro Vespignani
Affiliations

Modeling users' activity on twitter networks: validation of Dunbar's number

Bruno Gonçalves et al. PLoS One. 2011.

Abstract

Microblogging and mobile devices appear to augment human social capabilities, which raises the question whether they remove cognitive or biological constraints on human communication. In this paper we analyze a dataset of Twitter conversations collected across six months involving 1.7 million individuals and test the theoretical cognitive limit on the number of stable social relationships known as Dunbar's number. We find that the data are in agreement with Dunbar's result; users can entertain a maximum of 100-200 stable relationships. Thus, the 'economy of attention' is limited in the online world by cognitive and biological constraints as predicted by Dunbar's theory. We propose a simple model for users' behavior that includes finite priority queuing and time resources that reproduces the observed social behavior.

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Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.

Figures

Figure 1
Figure 1. Reply trees and user network.
A) The set of all trees is a forest. Each time a user replies, the corresponding tweet is connected to another one, resulting in a tree structure. B) Combining all the trees in the forest and projecting them onto the users results in a directed and weighted network that can be used as a proxy for relationships between users. The number of outgoing (incoming) connections of a given user is called the out (in) degree and is represented by kout (kin). The number of messages flowing along each edge is called the degree, w. The probability density function P(kout) (P(kint)) indicates the probability that any given node has kout (kin) out (in) degree and it is called the out (in) degree distribution and is a measure of node diversity on the network.
Figure 2
Figure 2. Connection weight and Reciprocated connections.
A) Out-weight as a function of the out-degree. The average weight of each outward connection gradually increases until it reaches a maximum near 150–200 contacts, signaling that a maximum level of social activity has been reached. Above this point, an increase in the number of contacts can no longer be sustained with the same amount of dedication to each. The red line corresponds to the average out-weight, while the gray shaded area illustrates the 50% confidence interval. B) Number of reciprocated connections, ρ, as a function of kin. As the number of people demanding our attention increases, it will eventually saturate our ability to reply leading to the flat behavior displayed in the dashed region.
Figure 3
Figure 3. Result of running our model on a heterogeneous network made of N = 105, nodes with degree distribution with γ = -2.4 and σ = 10.
Different curves correspond to different queue size. The inset shows the linear dependence of the peak on the queue size q. Each curve is the median of 1,000 to 2,000 runs of T = 2×104 time steps. In the inset, we plot the position of the peak as a function of the queue size. The linear relation is clear.
Figure 4
Figure 4. Results for the single user and different values of σ, the inter-user queue size variance.
We fixed the average queue size at qmax,i = 50 and extracted the priorities of user neighbors from a power-law statistical distribution with exponent γ = −2.1. For each ki we run T = 500 time steps and present the medians among 103 runs.
See this image and copyright information in PMC

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