Exact Median Graph Computation Via Graph Embedding

Given a set of graphs, the median graph is defined as the graph which has the smallest sum of distances (SOD) to all the graphs in the set. It has been proposed as a tool to obtain the representative of such a set. In spite of its potential applications, the existing algorithms are computationally complex and have a very limited applicability. In this paper we propose a new approach for the exact computation of the median graph based on graph embedding in vector spaces. Graphs are embedded into a vector space and the median is computed in the vector domain. After that, the median graph is recovered from this median vector. Experiments on a synthetic database show that our approach outperforms the previous existing exact algorithms both on computation time and number of SOD computations.