![]() Want more? See this analysis of shuffling algorithms using matrix diagrams. Matrix cells can also be encoded to show additional data here color depicts clusters computed by a community-detection algorithm. Line crossings are impossible with matrix views. As networks get large and highly connected, node-link diagrams often devolve into giant hairballs of line crossings. While path-following is harder in a matrix view than in a node-link diagram, matrices have other advantages. Jacques Bertin (or more specifically, his fleet of assistants) did this by hand with paper strips. This type of diagram can be extended with manual reordering of rows and columns, and expanding or collapsing of clusters, to allow deeper exploration. In the special case of a finite simple graph, the adjacency matrix is a (0,1)-matrix with zeros on its diagonal. In particular, the eigenvalues and eigenvectors of the adjacency matrix can be used to infer properties such as bipartiteness, degree of connectivity, structure of the automorphism group, and many others. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. In this chapter, we introduce the adjacency matrix of a graph which can be used to obtain structural properties of a graph. This example lets you try different orderings via the drop-down menu. In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. ![]() Given this two-dimensional representation of a graph, a natural visualization is to show the matrix! However, the effectiveness of a matrix diagram is heavily dependent on the order of rows and columns: if related nodes are placed closed to each other, it is easier to identify clusters and bridges. ![]() Here, vertices represent characters in a book, while edges represent co-occurrence in a chapter. Use the drop-down menu to reorder the matrix and explore the data.Ī network can be represented by an adjacency matrix, where each cell ij represents an edge from vertex i to vertex j. This matrix diagram visualizes character co-occurrences in Victor Hugo’s Les Misérables.Įach colored cell represents two characters that appeared in the same chapter darker cells indicate characters that co-occurred more frequently. Les Misérables Co-occurrence ApMike Bostock Les Misérables Co-occurrence ![]()
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