Sequential locality of graphs and its hypothesis testing

The adjacency matrix is the most fundamental and intuitive object in graph analysis that useful not only mathematically but also for visualizing structures of graphs. Because appearance an critically affected by ordering rows columns, or vertex ordering, statistical assessment graphs together with their sequences important identifying characteristic In this paper, we propose a hypothesis testing framework assesses how locally vertices are connected to each other along specified sequence, which provides foundation optimization problem called envelope reduction minimum linear arrangement. proposed tests particularly suitable moderately small data formulated based on combinatorial approach block model intrinsic ordering.