Getting started: usage

We provide a case study of the Fast Graphlet Transform, using Karate club, a small real-world dataset.

Prerequisites

You need to install the following packages for this demo.

pip install pyfglt networkx matplotlib seaborn

Karate Club

We will use Zachary’s Karate Club graph for the demonstration.

Zachary W. (1977). An information flow model for conflict and fission in small groups. Journal of Anthropological Research, 33, 452-473.

Load network

import networkx as nx
import matplotlib.pyplot as plt

seed = 0  # seed random number generators for reproducibility

G = nx.karate_club_graph()

pos = nx.spring_layout(G, seed=seed)

fig, ax = plt.subplots()

nx.draw_networkx_nodes(G, pos, ax=ax, node_size=20)
nx.draw_networkx_edges(G, pos, ax=ax, alpha=0.4)

plt.show()

Compute fast graphlet transform

Table 1: Astronomical object

import pyfglt.fglt as fg

F = fg.compute(G)

The returned object is a dataframe where rows correspond to nodes and columns to the 16 graphlets up to 4-node graphlets. For example, we can see the number of each graphlet incident to the first 5 nodes:

F.head()

Node id (0-based)	[0] vertex (==1)	[1] degree	[2] 2-path	[3] bifork	[4] 3-cycle	[5] 3-path, end	[6] 3-path, interior	[7] claw, leaf	[8] claw, root	[9] paw, handle	[10] paw, base	[11] paw, center	[12] 4-cycle	[13] diamond, off-cord	[14] diamond, on-cord	[15] 4-clique
0	1	16	17	102	18	81	197	13	352	6	34	171	10	2	30	7
1	1	9	19	24	12	73	56	33	32	8	80	27	6	2	18	7
2	1	10	34	34	11	72	179	84	54	17	75	51	20	6	8	7
3	1	6	20	5	10	49	11	56	1	5	81	5	0	4	7	7
4	1	3	16	1	2	17	1	64	0	15	25	0	1	2	1	0

Visualize graphlet distributions

import seaborn as sns
pg = sns.PairGrid(F.iloc[:,1:5])
pg.map_diag(sns.histplot, fill=False, bins = 20)
pg.map_upper(sns.scatterplot)
pg.map_lower(sns.histplot, bins = 20)

Node id (0-based)	[0] vertex (==1)	[1] degree	[2] 2-path	[3] bifork	[4] 3-cycle	[5] 3-path, end	[6] 3-path, interior	[7] claw, leaf	[8] claw, root	[9] paw, handle	[10] paw, base	[11] paw, center	[12] 4-cycle	[13] diamond, off-cord	[14] diamond, on-cord	[15] 4-clique
0	1	16	17	102	18	81	197	13	352	6	34	171	10	2	30	7
1	1	9	19	24	12	73	56	33	32	8	80	27	6	2	18	7
2	1	10	34	34	11	72	179	84	54	17	75	51	20	6	8	7
3	1	6	20	5	10	49	11	56	1	5	81	5	0	4	7	7
4	1	3	16	1	2	17	1	64	0	15	25	0	1	2	1	0

Node id (0-based)	[0] vertex (==1)	[1] degree	[2] 2-path	[3] bifork	[4] 3-cycle	[5] 3-path, end	[6] 3-path, interior	[7] claw, leaf	[8] claw, root	[9] paw, handle	[10] paw, base	[11] paw, center	[12] 4-cycle	[13] diamond, off-cord	[14] diamond, on-cord	[15] 4-clique
0	1	16	17	102	18	81	197	13	352	6	34	171	10	2	30	7
1	1	9	19	24	12	73	56	33	32	8	80	27	6	2	18	7
2	1	10	34	34	11	72	179	84	54	17	75	51	20	6	8	7
3	1	6	20	5	10	49	11	56	1	5	81	5	0	4	7	7
4	1	3	16	1	2	17	1	64	0	15	25	0	1	2	1	0

Node id (0-based)	[0] vertex (==1)	[1] degree	[2] 2-path	[3] bifork	[4] 3-cycle	[5] 3-path, end	[6] 3-path, interior	[7] claw, leaf	[8] claw, root	[9] paw, handle	[10] paw, base	[11] paw, center	[12] 4-cycle	[13] diamond, off-cord	[14] diamond, on-cord	[15] 4-clique
0	1	16	17	102	18	81	197	13	352	6	34	171	10	2	30	7
1	1	9	19	24	12	73	56	33	32	8	80	27	6	2	18	7
2	1	10	34	34	11	72	179	84	54	17	75	51	20	6	8	7
3	1	6	20	5	10	49	11	56	1	5	81	5	0	4	7	7
4	1	3	16	1	2	17	1	64	0	15	25	0	1	2	1	0