2,936 research outputs found
Constructing Adjacency Arrays from Incidence Arrays
Graph construction, a fundamental operation in a data processing pipeline, is
typically done by multiplying the incidence array representations of a graph,
and , to produce an adjacency
array of the graph, , that can be processed with a variety of
algorithms. This paper provides the mathematical criteria to determine if the
product
will have the required structure of the adjacency array of the graph. The
values in the resulting adjacency array are determined by the corresponding
addition and multiplication operations used to perform the
array multiplication. Illustrations of the various results possible from
different and operations are provided using a small
collection of popular music metadata.Comment: 8 pages, 5 figures, accepted to IEEE IPDPS 2017 Workshop on Graph
Algorithm Building Block
Ideal bases in constructions defined by directed graphs
The present article continues the investigation of visible ideal bases in constructions defined using directed graphs. Our main theorem establishes that, for every balanced digraph D and each idempotent semiring R with 1, the incidence semiring ID(R) of the digraph D has a convenient visible ideal basis BD(R). It also shows that the elements of BD(R) can always be used to generate two-sided ideals with the largest possible weight among the weights of all two-sided ideals in the incidence semiring
Ideal Basis in Constructions Defined by Directed Graphs
The present article continues the investigation of visible ideal bases in constructions defined using directed graphs. This notion is motivated by its applications for the design of classication systems. Our main theorem establishes that, for every balanced digraph and each idempotent semiring with identity element, the incidence semiring of the digraph has a convenient visible ideal basis. It also shows that the elements of the basis can always be used to generate ideals with the largest possible weight among the weights of all ideals in the incidence semiring
- β¦