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 a low clustering coefficient?

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 [2] . 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.