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average_neighbor_degree(G, source='out', target='out', nodes=None, weight=None)

In an undirected graph, the neighborhood :None:None:`N(i)` of node i contains the nodes that are connected to i by an edge.

For directed graphs, :None:None:`N(i)` is defined according to the parameter :None:None:`source`:

if source is 'in', then :None:None:`N(i)` consists of predecessors of node i.

if source is 'out', then :None:None:`N(i)` consists of successors of node i.

if source is 'in+out', then :None:None:`N(i)` is both predecessors and successors.

The average neighborhood degree of a node i is

$$k_{nn,i} = \frac{1}{|N(i)|} \sum_{j \in N(i)} k_j$$

where :None:None:`N(i)` are the neighbors of node i and :None:None:`k_j` is the degree of node :None:None:`j` which belongs to :None:None:`N(i)`. For weighted graphs, an analogous measure can be defined ,

$$k_{nn,i}^{w} = \frac{1}{s_i} \sum_{j \in N(i)} w_{ij} k_j$$

where :None:None:`s_i` is the weighted degree of node i, :None:None:`w_{ij}` is the weight of the edge that links i and :None:None:`j` and :None:None:`N(i)` are the neighbors of node i.

Parameters

G : NetworkX graph
source : string ("in"|"out"|"in+out"), optional (default="out"): Directed graphs only. Use "in"- or "out"-neighbors of source node.
target : string ("in"|"out"|"in+out"), optional (default="out"): Directed graphs only. Use "in"- or "out"-degree for target node.
nodes : list or iterable, optional (default=G.nodes): Compute neighbor degree only for specified nodes.
weight : string or None, optional (default=None): The edge attribute that holds the numerical value used as a weight. If None, then each edge has weight 1.

Raises

NetworkXError: If either :None:None:`source` or :None:None:`target` are not one of 'in', 'out', or 'in+out'. If either :None:None:`source` or :None:None:`target` is passed for an undirected graph.

Returns

d: dict: A dictionary keyed by node to the average degree of its neighbors.

Returns the average degree of the neighborhood of each node.

Examples

>>> G = nx.path_graph(4)
... G.edges[0, 1]["weight"] = 5
... G.edges[2, 3]["weight"] = 3

>>> nx.average_neighbor_degree(G)
{0: 2.0, 1: 1.5, 2: 1.5, 3: 2.0}

>>> nx.average_neighbor_degree(G, weight="weight")
{0: 2.0, 1: 1.1666666666666667, 2: 1.25, 3: 2.0}

>>> G = nx.DiGraph()
... nx.add_path(G, [0, 1, 2, 3])
... nx.average_neighbor_degree(G, source="in", target="in")
{0: 0.0, 1: 0.0, 2: 1.0, 3: 1.0}

>>> nx.average_neighbor_degree(G, source="out", target="out")
{0: 1.0, 1: 1.0, 2: 0.0, 3: 0.0}

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

networkx.algorithms.assortativity.connectivity.average_degree_connectivity networkx.algorithms.assortativity.neighbor_degree.average_neighbor_degree

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