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This paper proposes a metric to measure the dissimilarity between graphs thatmay have a different number of nodes. The proposed metric extends thegeneralised optimal subpattern assignment (GOSPA) metric, which is a metric forsets, to graphs. The proposed graph GOSPA metric includes costs associated withnode attribute errors for properly assigned nodes, missed and false nodes andedge mismatches between graphs. The computation of this metric is based onfinding the optimal assignments between nodes in the two graphs, with thepossibility of leaving some of the nodes unassigned. We also propose a lowerbound for the metric, which is also a metric for graphs and is computable inpolynomial time using linear programming. The metric is first derived forundirected unweighted graphs and it is then extended to directed and weightedgraphs. The properties of the metric are demonstrated via simulated andempirical datasets.

Graph GOSPA metric: a metric to measure the discrepancy between graphs of different sizes