Compute Katz centralities:

Highlight:

Rank vertices by centrality; higher value means more influence:

KatzCentrality works with undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

Use rules to specify the graph:

Use weights:

Nondefault initial centralities:

KatzCentrality works with large graphs:

Rank vertices of a graph by their importance in their reachable neighborhood:

Highlight the Katz centrality for CycleGraph:

GridGraph:

CompleteKaryTree:

PathGraph:

Simulate a citation network:

Find the top five most important papers and highlight them:

Predict a partition of the Zachary karate club in case of a conflict between influential members:

Show the partition:

Find the most common ancestor in a family tree:

Find descendants at the bottom of the tree:

In a trust network among employees, select employees who could efficiently spread the corporate culture:

Employees who are less likely to influence others:

The centrality vector satisfies the equation :

EigenvectorCentrality is a special case of KatzCentrality:

Take and with the largest eigenvalue of the adjacency matrix:

As , all vertices get the same centrality:

Use VertexIndex to obtain the centrality of a specific vertex: