In contrast, Personalized PageRank, which is a variant of PageRank, assigns a biased jump probability to each node and ranks graph nodes based on the graph structure.
This result extends to a class of higher-rank graph algebras which includes higher-rank graphs with a single vertex.
We close with a number of examples which illustrate why our question is so much more difficult for higher-rank graphs than for ordinary graphs.
We show that it is not in general sufficient, but that it is sufficient for higher-rank graphs with finitely many vertices.
They also give interesting conditions for topological higher rank graphs and P-graphs, and apply to the new Cuntz C⁎-algebra QN arising from the "ax+b -semigroup over N.
C ∗ -algebras of higher rank graphs were formalized in [73] (2000); the corresponding Kumjian Pask algebras were introduced in [40] (2014).
See Additional files 1 and 2 for the complete table and detailed per method rank graphs.
To quantify this, and rank graphs in terms of how closer to a maximal clique they were brought, we defined a connectivity coefficient, C, in Materials and Methods.
To design a cost function for ranking graphs, two disjoint sets, called parents P i and descendants D i, are defined Eq(3 -Eq(5).
We investigate the question: when is a higher-rank graph C⁎-algebra approximately finite-dimensional?
