A visual canonical adjacency matrix for graphs

Graph data mining algorithms rely on graph canonical forms to compare different graph structures. These canonical form definitions depend on node and edge labels. In this paper, we introduce a unique canonical visual matrix representation that only depends on a graph's topological information, so that two structurally identical graphs will have exactly the same visual adjacency matrix representation. In this canonical matrix, nodes are ordered based on a Breadth-First Search spanning tree. Special rules and filters are designed to guarantee the uniqueness of an arrangement. Such a unique matrix representation provides persistence and a stability which can be used and harnessed in visualization, especially for data exploration and studies.