Several concepts borrowed from graph theory are routinely used to better understand the inner workings of the (human) brain. To this end, a connectivity network of the brain is built first, which then allows one to assess quantities such as information flow and information routing via shortest path and maximum flow computations. Since brain networks typically contain several thousand nodes and edges, computational scaling is a key research area. In this contribution, we focus on approximate maximum flow computations in large brain networks. By combining graph partitioning with maximum flow computations, we propose a new approximation algorithm for the computation of the maximum flow with runtime O(|V||E|^2/k^2) compared to the usual runtime of O(|V||E|^2) for the Edmonds-Karp algorithm, where $V$ is the set of vertices, $E$ is the set of edges, and $k$ is the number of partitions. We assess both accuracy and runtime of the proposed algorithm on simulated graphs as well as on graphs downloaded from the Brain Networks Data Repository (https://networkrepository.com).

翻译：图论中的若干概念常被用于更好地理解（人类）大脑的内部工作机制。为此，首先构建大脑的连接网络，进而通过最短路径和最大流计算来评估信息流和信息路由等量。由于大脑网络通常包含数千个节点和边，计算可扩展性是一个关键研究领域。在本研究中，我们专注于大型大脑网络中的近似最大流计算。通过将图划分与最大流计算相结合，我们提出了一种新的近似算法用于计算最大流，其运行时间为O(|V||E|²/k²)，而Edmonds-Karp算法的常规运行时间为O(|V||E|²)，其中$V$为顶点集，$E$为边集，$k$为划分数量。我们在模拟图以及从大脑网络数据仓库（https://networkrepository.com）下载的图上评估了所提算法的准确性和运行时间。