average_neighbor_degree#
- average_neighbor_degree(G, source='out', target='out', nodes=None, weight=None)[source]#
Returns the average degree of the neighborhood of each node.
In an undirected graph, the neighborhood
N(i)
of nodei
contains the nodes that are connected toi
by an edge.For directed graphs,
N(i)
is defined according to the parametersource
:if source is ‘in’, then
N(i)
consists of predecessors of nodei
.if source is ‘out’, then
N(i)
consists of successors of nodei
.if source is ‘in+out’, then
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
N(i)
are the neighbors of nodei
andk_j
is the degree of nodej
which belongs toN(i)
. For weighted graphs, an analogous measure can be defined [1],\[k_{nn,i}^{w} = \frac{1}{s_i} \sum_{j \in N(i)} w_{ij} k_j\]where
s_i
is the weighted degree of nodei
,w_{ij}
is the weight of the edge that linksi
andj
andN(i)
are the neighbors of nodei
.- Parameters
- GNetworkX graph
- sourcestring (“in”|”out”|”in+out”), optional (default=”out”)
Directed graphs only. Use “in”- or “out”-neighbors of source node.
- targetstring (“in”|”out”|”in+out”), optional (default=”out”)
Directed graphs only. Use “in”- or “out”-degree for target node.
- nodeslist or iterable, optional (default=G.nodes)
Compute neighbor degree only for specified nodes.
- weightstring 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.
- Returns
- d: dict
A dictionary keyed by node to the average degree of its neighbors.
- Raises
- NetworkXError
If either
source
ortarget
are not one of ‘in’, ‘out’, or ‘in+out’. If eithersource
ortarget
is passed for an undirected graph.
See also
References
- 1
A. Barrat, M. Barthélemy, R. Pastor-Satorras, and A. Vespignani, “The architecture of complex weighted networks”. PNAS 101 (11): 3747–3752 (2004).
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}