Theoretical and Computational Neuroscience
Author: Dalma Bilbao | Email: bilbaodalmaanahi@gmail.com
Dalma.A Bilbao 1°, Diego .M Mateos 1°, Hugo. A Aimar 1°
1° IMAL -CONICET
In the analysis of relationships in systems, graph theory represents connections, but limited to pairs. In reality, the relationships are more complex and the graphs representation loses information. Thus, hypergraphs emerge as a natural extension, proposed by Claude Berge in 1960, to capture these complex relationships. A hypergraph is a pair H(V,E) with vertices and hyperedges covering V. We propose a model based on relationships of graphs with similar vertices but different
connections. For example, friendships in social networks, routes between cities or brain connections in different frequencies. Taking m graphs Gi=(W,Ei), i= 1,..,m
with cardinality W=k, we create a hypergraph with p=k(k-1)/k vertices and m hyperedges. Laplacian analysis and centrality quantify the hypergraph, revealing its structure and properties. We applied this to real data, analyzing brain connectivity in rats with iEEG in different sleep states. Vertices (k=6 iEEG channels) and graphs Gi (delta, theta, alpha, beta, gamma) form state-specific hypergraphs, allowing comparison.