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Graphs and Graph Routines

The library only provides a few tools for graphs, related to algorithms for bandwith reduction, such as the calculation of pseudo peripheral nodes and rooted level structures.

The Graph class is a subclass of the Graph class from networkx, with a few additions.

from sigmaepsilon.math.graph import Graph
import networkx as nx

grid = nx.grid_2d_graph(5, 5)  # 5x5 grid
G = Graph(grid)

One of these additions is that it is possible to get the adjacency matrix of a graph directly, by calling the adjacency_matrix method of an instance. The method returns a Numba-jittable instance of the csr_matrix class from sigmaepsilon.math.linalg, hence making the graph instance itself sort of Numba-jittable as well.

G.adjacency_matrix()

<Compressed Sparse Row sparse array of dtype 'int32'
        with 80 stored elements and shape (25, 25)>

The Graph class in sigmaepsilon.math.graph is also equipped with methods for the calculation of pseudo peripheral nodes and rooted level structures.

G.pseudo_peripheral_nodes()

array([24,  0], dtype=int64)

G.rooted_level_structure()

DictType[int64,array(int64, 1d, C)]<iv=None>({0: [0], 1: [1 5], 2: [ 2  6 10], 3: [ 3  7 11 15], 4: [ 4  8 12 16 20], 5: [ 9 13 17 21], 6: [14 18 22], 7: [19 23], 8: [24]})