# MeanNeighborDegree

gives a list of mean neighbor degrees of vertices for the graph g.

MeanNeighborDegree[g,"In"]

gives a list of mean neighbor in-degrees.

MeanNeighborDegree[g,"Out"]

gives a list of mean neighbor out-degrees.

MeanNeighborDegree[{vw,},]

uses rules vw to specify the graph g.

# Details • The mean neighbor degree is also known as the average neighbor degree.
• The mean neighbor degree of the vertex is the mean of vertex degrees of neighbors of .
• For weighted graphs, the mean neighbor degree of the vertex is given by over all neighbors of with edge weight between and . is the degree of the vertex and is the total of weights .
• MeanNeighborDegree works with undirected graphs, directed graphs, weighted graphs, multigraphs, and mixed graphs.

# Examples

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## Basic Examples(2)

Compute mean neighbor degrees:

Highlight:

Rank the vertices. Highest-ranked vertices are adjacent to high-degree vertices:

## Scope(8)

MeanNeighborDegree works with undirected graphs:

Directed graphs:

Weighted graphs:

Multigraphs:

Mixed graphs:

Use rules to specify the graph:

Compute the mean neighbor in- and out-degree:

MeanNeighborDegree works with large graphs:

## Applications(4)

Find the average number of connections for the internet at the level of autonomous systems:

The presence of high-degree hubs in the network increases the mean neighbor degree:

A citation network from the High Energy Physics Phenomenology section of the arXiv e-Print archive. Compute the average number of citations per article:

The mean number of citing articles for citations:

Compute the average number of references:

The mean number of cited articles for references:

Highlight social hubs in the Zachary karate club network:

A social network of frequent association ties between dolphins living off Doubtful Sound, NZ:

Compute the probability that a dolphin with just one tie has a neighbor with nine ties or more:

Find the probability in a derived model:

## Properties & Relations(4)

Isolated vertices have mean neighbor degree 0:

Directed edges are treated as undirected:

Use VertexDegree to compute the mean neighbor degree:

MeanDegreeConnectivity gives the means over vertices gathered by degree:

Find the 3-mean degree connectivity:

Find vertices of degree 3:

The mean of mean neighbor degrees: