A Clustering Coefficient Calculator helps measure how interconnected the nodes of a network are, either locally or globally. It is a crucial tool in network analysis, often used in social sciences, biology, computer networks, and physics. The local clustering coefficient evaluates how a single node’s neighbors connect to each other, while the global clustering coefficient assesses the overall clustering of the network. Understanding clustering coefficients provides insights into the network’s efficiency, robustness, and group dynamics.
Formula of Clustering Coefficient Calculator
Local Clustering Coefficient:
C(v) = 2 * T(v) / (k(v) * (k(v) – 1))
Where:
C(v) is the local clustering coefficient of a node v.
T(v) is the number of triangles node v is a part of.
k(v) is the degree of node v (number of neighbors).
Global Clustering Coefficient:
C = 3 * T / (3 * T + 2 * L)
Where:
C is the global clustering coefficient.
T is the number of triangles in the network.
L is the number of connected triples (paths of length 2).
General Terms and Reference Table
Below is a table with common terms and references to help interpret clustering coefficient values:
| Term | Definition | Example Usage |
|---|---|---|
| Local Clustering Coefficient | Proportion of connections between a node’s neighbors relative to the possible connections. | Used to measure tight-knit groups in a social network. |
| Global Clustering Coefficient | Overall clustering of the network, considering all nodes. | Useful in analyzing the efficiency of a power grid. |
| Triangle (T) | A set of three nodes, all of which are interconnected. | Friendship circles in a social network. |
| Connected Triple (L) | A set of three nodes where at least two are connected. | Pathways in a transport network. |
Example of Clustering Coefficient Calculator
Consider a small network where a node v has 4 neighbors, with 3 of them interconnected to form triangles. To calculate the local clustering coefficient for this node:
k(v) = 4 (degree of node v)
T(v) = 3 (triangles involving v)
Using the formula:
C(v) = 2 * 3 / (4 * (4 – 1))
C(v) = 6 / 12 = 0.5 or 50%
This means 50% of the node’s neighbors are interconnected.
For the global clustering coefficient, suppose there are 10 triangles (T) and 15 connected triples (L) in the entire network. The calculation would be:
C = 3 * 10 / (3 * 10 + 2 * 15)
C = 30 / 60 = 0.5 or 50%
This value indicates that 50% of all possible connections between triples form triangles in the network.
Most Common FAQs
The clustering coefficient helps analyze the interconnectedness of a network. High values indicate a dense or tightly connected network, while low values suggest sparsely connected nodes.
The local clustering coefficient measures the clustering around a single node, while the global clustering coefficient evaluates the overall clustering of the entire network.
No, the clustering coefficient ranges between 0 and 1, where 1 represents a fully interconnected group of neighbors and 0 indicates no clustering.