1. What is Average Degree?

Average Degree is defined as the product of number of edges incident on a node and the probability of the pair being connected. It represents the average number of connections per node in a network.

2. How Does the Calculator Work?

The calculator uses the Average Degree formula:

Where:

• \( k \) — Average Degree
• \( p \) — Node Connection Probability (0-1)
• \( N \) — Number of Nodes

Explanation: The formula calculates the average number of connections per node by multiplying the connection probability by the total number of nodes.

3. Importance of Average Degree Calculation

Details: Average degree is a fundamental metric in network analysis that helps understand the connectivity and density of networks. It's crucial for analyzing social networks, computer networks, biological networks, and other complex systems.

4. Using the Calculator

Tips: Enter node connection probability (value between 0-1) and number of nodes (positive integer). All values must be valid (0 ≤ p ≤ 1, N ≥ 1).

5. Frequently Asked Questions (FAQ)

Q1: What does a high average degree indicate?
A: A high average degree indicates a densely connected network where nodes have many connections to other nodes.

Q2: How is average degree different from degree distribution?
A: Average degree gives a single summary statistic, while degree distribution shows the full range and frequency of different degree values in the network.

Q3: What are typical average degree values in real networks?
A: Values vary widely depending on network type. Social networks often have average degrees in the tens or hundreds, while sparse networks might have average degrees close to 1.

Q4: Can average degree be greater than N-1?
A: No, in a simple graph without self-loops, the maximum degree for any node is N-1, so average degree cannot exceed N-1.

Q5: How does average degree relate to network density?
A: Network density is equal to average degree divided by (N-1), showing the proportion of possible connections that actually exist.