Degree Distribution

Introduction

Degree distribution is a measure that helps us understand the overall structure and behavior of a network or graph by showing the frequency of nodes with a specific degree. By examining the degree distribution, we can gain insights into the connectivity patterns and identify the characteristics of the network. In other words, it is a probability distribution of the degrees over the entire network.

Degree distribution can be applied to various domains, such as social networks, biological networks, and transportation systems, to gain insights into the structure and behavior of these networks, identify potential vulnerabilities, and make informed decisions for resource allocation, targeted interventions, or network optimization.

Difference between degree centrality and degree distribution

Degree centrality and degree distribution are two related concepts in the field of network analysis, which is the study of complex networks and their properties. They are used to characterize nodes within a network and understand the overall structure of the network, respectively.

Degree centrality: Degree centrality tells us how well-connected a node is. In a directed network, where connections have a direction, degree centrality can be further divided into in-degree centrality (number of incoming connections) and out-degree centrality (number of outgoing connections).

Degree distribution: Degree distribution shows the proportion of nodes with a certain degree in the network. Degree distribution helps us understand the overall structure of the network and identify patterns.

Calculate degree distribution

To calculate the degree distribution for the given network and plot the graph, we can use Python with the NetworkX library for network analysis and matplotlib for plotting: