Reducing the influence of intramodular connectivity in participation coefficient

Both natural and engineered networks are often modular. Whether a network node interacts with only nodes from its own module or nodes from multiple modules provides insight into its functional role. The participation coefficient (PC) is typically used to measure this attribute, although its value also depends on the size and connectedness of the module it belongs to and may lead to nonintuitive identification of highly connected nodes. Here, we develop a normalized PC that reduces the influence of intramodular connectivity compared with the conventional PC. Using brain, C. elegans, airport, and simulated networks, we show that our measure of participation is not influenced by the size or connectedness of modules, while preserving conceptual and mathematical properties, of the classic formulation of PC. Unlike the conventional PC, we identify London and New York as high participators in the air traffic network and demonstrate stronger associations with working memory in human brain networks, yielding new insights into nodal participation across network modules.