Date Published: May 23, 2019
Publisher: Public Library of Science
Author(s): C. Ben Gibson, Norbou Buchler, Blaine Hoffman, Claire-Genevieve La Fleur, Rodrigo Huerta-Quintanilla.
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.
Fundamental to the prediction of network phenomena is an explanation of heavy-tailed degree distributions—the enumeration of links among individuals in a network. Indeed, many observations of social networks and communication networks in particular is that the emergent degree distribution of emergent degree is “non-normal” and heavy-tailed . In many systems, a few individuals dominate counts of network interactions and have very many links, whereas most individuals have just a few links. Researchers have observed such long-tailed, approximate Pareto-distributed degree distributions in a number of social networks [2–5], including human communication networks [6, 7]. The ubiquity of this observed approximate Pareto distribution has been of considerable interest to social scientists, as it deviates from Poisson-distributed counts that would normally be associated with random chance. Often, Pareto-distributed degree is explained by researchers via preferential attachment, which, under certain conditions, can create power law distributions. [8–12]; however, in conditions where the network has no growth in the number of nodes, preferential attachment instead converges to a complete graph . Explanations of long-tailed degree in networks without growth thus still requires explanation.
Army Research Lab IRB approved the following study; verbal consent was granted by participants. The military organization addressed specific problems that occurred in simulation and during mission execution over a two week period as they conducted both military and civil-military operations. This dataset reflects the operations of a work-directed networked organization functioning as a purposive social system where staff members are readily known to one another by role and position and work collaboratively to accomplish one or more common objectives . The responsibility for accomplishing the various tasks and sub-tasks were divided and assigned among the staff and included monitoring key events, analyzing information, adhering to work routines, developing work products, and coordinating an effective response, given resource limitations.
REM parameter results are listed in Table 2. The strongest are normalized indegree affecting future sending (NIDSnd) and receiving (NIDRec) rates. These are traditionally referred to as preferential attachment—effects that represent individuals being drawn into the conversation through repeated interactions. We note that though these are the strongest effects in the model, they do not recreate the exact degree distribution in simulations, as predicted by . Second, normalized out-degree effects (NODSnd and NODRec) are strong for future sending rate, but not for future receiving rates. Though individuals may decide to send many messages into the network, it does not affect how many they receive in the future. Recency-receive effect (RRecSnd) is a dyadic-level effect that puts a rank-ordered response priority on recency of messages sent to person i from others in the network. For example, the last person to send a message to person i is scored a 1, the second-to-last person to send person i a message is scored a 1/2, and so on. Recency-send effect (RSndSnd) is a rank-ordered send priority from i to j when i has already sent emails to j in the past. Both of these effects have strong, positive coefficients in prediction of the next event in the series. Individual-level payrank and situational awareness also affected send rates positively; payrank was associated with future receive rates, but situational awareness was not. The greater the difference in payrank between actors, the more priority for response the lower-payrank actor gave to higher-payrank actors’ emails. Actors with lower situational awareness (SA) sent emails more often to those of higher SA than to those with the same or lower SA. As discussed above, most of the tested dyadic p-shifts were found to be significant and positive, the most powerful one being the AB-AY shift (the AB-AY shift also includes group emails). Residual deviance was 95712.11 on a null deviance was 173523.1 (AIC 95748.11).
Our models show many possible candidates for prediction of the degree distribution, as we found many significant ecological and individual-level attributes predicting communication dynamics (see Fig 4). However, out of all explanations we tested, dyadic turn-taking dynamics and turn-continuing dynamics best explain the long-tailed degree distributions found in an observed communications network. These two concepts—turn-taking and turn-continuing—are essential elements of coherent communications between humans [14, 16, 17]. In some cases, turn-continuing p-shifts are referred to as “burstiness”, and have been used as an explanation of other long-tailed distributions such as response waiting times in communications networks . The prevalence of these participation-shifts in social networks, combined with the prevalence of their long-tailed degree distributions, suggests a possible implicit link that should be investigated further using other communication network settings. Actor-level normalized indegree affecting future participation rates had strong effects in our model, but did not reproduce observed in- and outdegree distributions (see Fig 5(c) and 5(d)), as predicted in .
Long-tailed degree distributions are found among many social phenomena. Preferential attachment is the most common explanation, but have limitation in networks with a static number of nodes. We find that participation shifts—turn-taking and turn-continuing participation norms found in nearly all measured human communication networks—predicts degree distributions that match those of the observed network with an unchanging number of nodes. The prevalence of participation shifts in communication networks provides a viable explanation of long-tailed degree in many observed social networks, and should be considered in further investigations of similar settings.