As summer winds down, many residents of continental Europe are making their way back north. The long return journeys from the beaches of southern France, Spain, and Italy once again clog alpine tunnels and Mediterranean coastal routes during the infamous Black Saturday bottlenecks. This annual migration forms a network—not just of connections, but of communities shaped by shared patterns of origin and destination.
This is where network science—and in particular, community detection—comes into play. For decades, researchers have developed powerful tools to uncover communities in networks: clusters of tightly interconnected nodes. These tools work best for undirected networks, where connections are mutual. Graphically, this resembles node maps that many are familiar with, showing how groups of people might all be friends on Facebook or follow similar sports accounts.
Using a standard modularity algorithm, researchers can find connections between different communities and draw useful conclusions. For instance, users in the fly-fishing community might also appear as followers of non-alcoholic beer enthusiasts in Geneva. This type of information extraction, impossible without community analysis, provides a layer of meaning that can be leveraged for marketing or even influencing elections.
Challenges of Directed Networks
When it comes to directed networks—where influence, information, or traffic flows from one point to another—the concept of a “community” becomes much harder to define. Existing methods often ignore direction or use it inconsistently. However, a new study from EPFL and the University of Geneva redefines what a community means in a directed graph, capturing both who belongs together and how information flows between them.
Enter bimodularity. Researchers at Dimitri Van De Ville’s Laboratory of Medical Image Processing and Analysis have developed a groundbreaking method that adds directionality to network analysis. This allows them to detect not only which cities empty out in summer but also where these communities tend to go to find a beach and parasol.
“With bimodularity, we can finally distinguish senders from receivers in a network. That means finer-grained detail in how communities interact—who’s sending, and who’s receiving,” says Van de Ville.
Bicommunity Detection: A New Approach
Bimodularity allows for bicommunity detection, a unique approach that sets this method apart by identifying communities not by clustering nodes, but by clustering edges. Instead of asking which individuals belong together, the algorithm examines which interactions behave similarly in terms of directionality. This edge-based approach reveals pairs of communities: one that sends information and one that receives it, a new organizational structure called bicommunities.
Now, not only can we identify the community of nodes represented by red, blue, and yellow clusters with conventional community detection, but we can also detect a second type of community represented by directional arrows in green, orange, and purple. This provides a crucial new layer of information, revealing who is connected in each community and whether they are part of another community of senders or receivers, influencers or followers, commuters or vacationers.
Real-World Applications and Future Implications
While this discovery has not arrived in time to alleviate this year’s summer traffic jams, researchers are optimistic about its imminent implementation in network analysis across a wide range of applications. To test the theory, they applied it to a well-known dataset of neuronal activity from the roundworm C. elegans. The new algorithm not only organized the neural network in alignment with anatomical data but also revealed new groupings of neurons that shed light on functionality within the nervous system.
“What’s exciting is that bimodularity doesn’t just confirm the known flow from sensory input to motion—it also reveals the intermediate steps in between, like sensory to processing and processing to motion. These could point to causal pathways, opening up new possibilities for interpreting how information moves through the nervous system,” says first author and PhD student Alexandre Cionca.
This breakthrough in network theory has the potential to revolutionize our understanding of complex systems, from social networks to biological processes. By providing a more nuanced view of how communities interact, bimodularity could pave the way for advancements in fields as diverse as neuroscience, marketing, and urban planning.
