# What does the clustering coefficient tell us?

October 10, 2019 Off By idswater

## What does the clustering coefficient tell us?

The clustering coefficient measures how connected a vertex’s neighbors are to one another. More specifically, it is calculated as: (the number of edges connecting a vertex’s neighbors)/(the total number of possible edges between the vertex’s neighbors).

## How do you interpret clustering coefficients?

Clustering coefficient is a property of a node in a network. Roughly speaking it tells how well connected the neighborhood of the node is. If the neighborhood is fully connected, the clustering coefficient is 1 and a value close to 0 means that there are hardly any connections in the neighborhood.

## How do you find the clustering coefficient of a graph?

Clustering coefficient is a local measure. Therefore we calculate clustering coefficient of a node by using following formula: Here, Ki is the degree of node i and Li is the number of edges between the ki neighbors of node i.

## What is average clustering coefficient?

The clustering coefficient for the whole graph is the average of the local values Ci C=1nn∑i=1Ci, where n is the number of nodes in the network. By definition 0≤Ci≤1 and 0≤C≤1. The clustering coefficient of a graph is closely related to the transitivity of a graph, as both measure the relative frequency of triangles.

## Can clustering coefficient be negative?

Green lines are positive and red lines are negative. Edge weights are ignored in the computation of the unweighted clustering coefficients and . In each triangle one edge is negative. Note however that it is irrelevant for the value of the signed clustering coefficients which of the three edges is the negative one.

## What is low clustering coefficient?

A low clustering coefficient is indicative of a network comprised of numerous weak ties. More precisely, the clustering coefficient of a node is the ratio of existing links connecting a node’s neighbors to each other to the maximum possible number of such links.

## What is the purpose of clustering coefficient?

The local clustering coefficient of a vertex (node) in a graph quantifies how close its neighbours are to being a clique (complete graph).

## What is local clustering?

Local clustering is like a local version of betweenness: where betweenness centrality measures a vertex’s control over information flowing between all pairs of nodes in its component, local clustering measures control over flows between just the immediate neighbors of a vertex.

## How does Louvain clustering work?

The Louvain method is an algorithm to detect communities in large networks. The Louvain algorithm is a hierarchical clustering algorithm, that recursively merges communities into a single node and executes the modularity clustering on the condensed graphs.

## How does the clustering coefficient work in real life?

Evidence suggests that in most real-world networks, and in particular social networks, nodes tend to create tightly knit groups characterised by a relatively high density of ties; this likelihood tends to be greater than the average probability of a tie randomly established between two nodes (Holland and Leinhardt, 1971; Watts and Strogatz, 1998 ).

## What is the local clustering coefficient of a directed graph?

For a directed graph, is distinct from , and therefore for each neighborhood there are links that could exist among the vertices within the neighborhood ( is the number of neighbors of a vertex). Thus, the local clustering coefficient for directed graphs is given as  . An undirected graph has the property that and are considered identical.

## Why do high degree nodes have lower clustering coefficient?

This means that nodes with a high degree will be overrepresented in variant 1, and underrepresented in variant 2. The correlation of both measures is thus a hint that nodes with high and low degree in general do not have the same local clustering coefficient. Let’s see: This plot needs some explanation.

## How is the clustering coefficient of a triangle calculated?

In the denominator, ki2 counts the number of edge pairs that vertex i is involved in plus the number of single edges traversed twice. ki is the number of edges connected to vertex i, and subtracting ki then removes the latter, leaving only a set of edge pairs that could conceivably be connected into triangles.