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
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- 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
open allclose allBasic Examples (2)
Scope (8)
MeanNeighborDegree works with undirected 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:
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:
Text
Wolfram Research (2012), MeanNeighborDegree, Wolfram Language function, https://reference.wolfram.com/language/ref/MeanNeighborDegree.html (updated 2015).
CMS
Wolfram Language. 2012. "MeanNeighborDegree." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/MeanNeighborDegree.html.
APA
Wolfram Language. (2012). MeanNeighborDegree. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MeanNeighborDegree.html