Graph Signal

Summary

the given signal is observed on a graph \({\cal G}:=({\cal V},{\cal E})\)

• \({\cal V}\) represents the set of nodes
• \({\cal E}\) represents the set of edges (links)
• we have observed a real-valued signal, denoted as \(y: V \to \mathbb{R}\)

Import

import numpy as np
import networkx as nx
import matplotlib.pyplot as plt

Graph Signal

Figure: A random positive graph signal on the vertices of the Petersen graph. The height of each blue bar represents the signal value at the vertex where the bar originates (Shuman et al. 2013)

Shuman, David I, Sunil K Narang, Pascal Frossard, Antonio Ortega, and Pierre Vandergheynst. 2013. “The Emerging Field of Signal Processing on Graphs: Extending High-Dimensional Data Analysis to Networks and Other Irregular Domains.” IEEE Signal Processing Magazine 30 (3): 83–98.

Suppose we have observed a real-valued signal, denoted as \(y: V \to \mathbb{R}\), from a graph \({\cal G} = (V, E)\), where \(V\) represents the set of nodes and \(E\) represents the set of edges.