Participation shifts explain degree distributions in a human communications network

Abstract

Human interpersonal communications drive political, technological, and economic systems, placing importance on network link prediction as a fundamental problem of the sciences. These systems are often described at the network-level by degree counts -the number of communication links associated with individuals in the network-that often follow approximate Pareto distributions, a divergence from Poisson-distributed counts associated with random chance. A defining challenge is to understand the inter-personal dynamics that give rise to such heavy-tailed degree distributions at the network-level; primarily, these distributions are explained by preferential attachment, which, under certain conditions, can create power law distributions; preferential attachment's prediction of these distributions breaks down, however, in conditions with no network growth. Analysis of an organization's email network suggests that these degree distributions may be caused by the existence of individual participation-shift dynamics that are necessary for coherent communication between humans. We find that the email network's degree distribution is best explained by turn-taking and turn-continuing norms present in most social network communication. We thus describe a mechanism to explain a long-tailed degree distribution in conditions with no network growth.

Fig 1. Coalition joint task force.

(a) (left) Organizational structure of the Coalition Joint Task Force during the two-week military training exercise held at the Mission Command Battle Laboratory (Fort Leavenworth, Kansas). The network organization spans multiple echelons from Joint Command to Division to Brigade to support Battalions. (right) The core units exercised during the training event and subjected to our analysis- the Mission Command staff of a U.S. Division and two sub-ordinate Brigades, a U.S. Heavy Brigade Combat Team and a U.K. Coalition Brigade Combat Team. Individual situation awareness data was collected from the participating staff of these three core units. (b) Example seating chart for the Mission Command staff of the U.S. Division.

Fig 2. Predicted network comparisons.

Preferential attachment and participation shifts as explanations of network structure in observed data. Figs (a)-(b) are simulated email networks using fitted parameters from a model including only preferential attachment and participation shifts, respectively. The network structure in simulated network (b) tends to resemble the observed network (c), though (a) is the typical explanation of long-tailed degree structure. 300 email events were simulated among 94 nodes.

Fig 3

(a) Predicted indegree distribution by participation shift type. Each prediction is drawn from a separate relational events model including only the participation shift shown. PSAB-BA best predicts the indegree distribution, but is not fully adequate to do so. (b) Predicted outdegree distribution by participation shift type. PSAB-AY participation shift perfectly reproduces the outdegree distribution without any other parameter.

Fig 4. Relational events modeling of email comms.

Parameters from a relational events model predicting sequential, dyadic communicative actions between actors in the network. The strongest effects (NIDSnd and NIDRec) represent preferential attachment, as those with greater indegree participate more in the future. The next strongest class of predictors are “burstiness” parameters (NODSnd and PSAB-AY). The effect size for PSAB-BA participation shift (turn-taking dynamics) is relatively smaller, but strong.

Fig 5

(a)-(b) CDF of observed versus predicted degree distributions (via relational events model) given only selected participation shifts (AB-BA, AB-BY, RecRecSnd) in the model. Predicted degree distributions match that of observed (KS test p > .05). (c)-(d) CDF of observed versus predicted degree distributions given only preferential attachment. Predicted degree distributions (via relational events model) did not match observed (KS test p < .001).