Finding influential subjects in a network using a causal framework

Abstract

Researchers across a wide array of disciplines are interested in finding the most influential subjects in a network. In a network setting, intervention effects and health outcomes can spill over from one node to another through network ties, and influential subjects are expected to have a greater impact than others. For this reason, network research in public health has attempted to maximize health and behavioral changes by intervening on a subset of influential subjects. Although influence is often defined only implicitly in most of the literature, the operative notion of influence is inherently causal in many cases: influential subjects are those we should intervene on to achieve the greatest overall effect across the entire network. In this work, we define a causal notion of influence using potential outcomes. We review existing influence measures, such as node centrality, that largely rely on the particular features of the network structure and/or on certain diffusion models that predict the pattern of information or diseases spreads through network ties. We provide simulation studies to demonstrate when popular centrality measures can agree with our causal measure of influence. As an illustrative example, we apply several popular centrality measures to the HIV risk network in the Transmission Reduction Intervention Project and demonstrate the assumptions under which each centrality can represent the causal influence of each participant in the study.

Keywords: causal inference; centrality; contagion; interference.

Figure 1.

The Transmission Reduction Intervention Project (Athens, Greece, 2013–2015) network of people who inject drugs and their contacts with red nodes representing the participants who received the community alert

Figure 2.

A hypothetical network with N = 10 nodes. The table in the right panel shows the centrality measures using degree, betweenness, and diffusion centralities. *Diffusion centralities were measured at p = 0.3 and T = 2.

Figure 3.

Each matrix contains 277 × 277 cells. Each cell illustrates how often the top $l$ of influential nodes established through each centrality metric are completely contained in the top $k$ causally influential nodes if $l⩾k$ (lower right corner); when $l<k$ (upper left corner) each cell represents how frequently the top $l$ in each centrality contains the top $k$ in $\tau$.

Figure 4.

The degree and betweenness centralities applied to the TRIP network. The nodes are shaded based on the 20-quantiles of each centrality metric, and a darker shading indicates higher centrality