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MeanDegreeConnectivity

MeanDegreeConnectivity[g]

gives a list of k-mean degree connectivity for the graph g for successive k=0,1,2… .

MeanDegreeConnectivity[g,"In"]

gives a list of k-mean in-degree connectivity for the graph g.

MeanDegreeConnectivity[g,"Out"]

gives a list of k-mean out-degree connectivity for the graph g.

MeanDegreeConnectivity[{vw,…},…]

uses rules vw to specify the graph g.

MeanDegreeConnectivity

MeanDegreeConnectivity[g]

gives a list of k-mean degree connectivity for the graph g for successive k=0,1,2… .

MeanDegreeConnectivity[g,"In"]

gives a list of k-mean in-degree connectivity for the graph g.

MeanDegreeConnectivity[g,"Out"]

gives a list of k-mean out-degree connectivity for the graph g.

MeanDegreeConnectivity[{vw,…},…]

uses rules vw to specify the graph g.

Details

The mean degree connectivity is also known as average degree connectivity and average nearest neighbor degree.
The k-mean degree connectivity is the average of the mean neighbor degrees of vertices of degree k.
MeanDegreeConnectivity[g] returns a list {m₀,m₁,…,m_d}, where m_k is the k-mean degree connectivity and d is the maximum vertex degree in g.
MeanDegreeConnectivity works with undirected graphs, directed graphs, weighted graphs, multigraphs, and mixed graphs.

Examples

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Basic Examples (2)

Compute the mean degree connectivity for a graph:

Wolfram Language code: MeanDegreeConnectivity[[image]]

Plot the mean degree connectivity:

Wolfram Language code: g = RandomGraph[SpatialGraphDistribution[100, 0.2]];

Wolfram Language code: ListPlot[Rest[MeanDegreeConnectivity[g]], Filling -> Axis]

Scope (8)

MeanDegreeConnectivity works with undirected graphs:

Wolfram Language code: MeanDegreeConnectivity[[image]]

Directed graphs:

Wolfram Language code: MeanDegreeConnectivity[[image]]

Weighted graphs:

Wolfram Language code: MeanDegreeConnectivity[[image]]

Multigraphs:

Wolfram Language code: MeanDegreeConnectivity[[image]]

Mixed graphs:

Wolfram Language code: MeanDegreeConnectivity[[image]]

Use rules to specify the graph:

Wolfram Language code: MeanDegreeConnectivity[{1 -> 2, 3 -> 1, 3 -> 2, 2 -> 3, 2 -> 4, 3 -> 4}]

Compute the mean in- and out-degree connectivity:

Wolfram Language code: MeanDegreeConnectivity[[image], "In"]

Wolfram Language code: MeanDegreeConnectivity[[image], "Out"]

MeanDegreeConnectivity works with large graphs:

Wolfram Language code: g = RandomGraph[{10 ^ 4, 10 ^ 5}];

Wolfram Language code: MeanDegreeConnectivity[g]//Shallow//Timing

Properties & Relations (1)

MeanDegreeConnectivity[g][[k+1]] gives the k-mean degree connectivity:

Wolfram Language code: g = CompleteGraph[{2, 4, 3}, VertexShapeFunction -> "Name"]

Wolfram Language code: MeanDegreeConnectivity[g][[8]]

It is a mean of MeanNeighborDegree:

Wolfram Language code: Mean[MeanNeighborDegree[g][[Table[VertexIndex[g, v], {v, {1, 2}}]]]]

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