Spaces:
Sleeping
Sleeping
| """ | |
| Vitality measures. | |
| """ | |
| from functools import partial | |
| import networkx as nx | |
| __all__ = ["closeness_vitality"] | |
| def closeness_vitality(G, node=None, weight=None, wiener_index=None): | |
| """Returns the closeness vitality for nodes in the graph. | |
| The *closeness vitality* of a node, defined in Section 3.6.2 of [1], | |
| is the change in the sum of distances between all node pairs when | |
| excluding that node. | |
| Parameters | |
| ---------- | |
| G : NetworkX graph | |
| A strongly-connected graph. | |
| weight : string | |
| The name of the edge attribute used as weight. This is passed | |
| directly to the :func:`~networkx.wiener_index` function. | |
| node : object | |
| If specified, only the closeness vitality for this node will be | |
| returned. Otherwise, a dictionary mapping each node to its | |
| closeness vitality will be returned. | |
| Other parameters | |
| ---------------- | |
| wiener_index : number | |
| If you have already computed the Wiener index of the graph | |
| `G`, you can provide that value here. Otherwise, it will be | |
| computed for you. | |
| Returns | |
| ------- | |
| dictionary or float | |
| If `node` is None, this function returns a dictionary | |
| with nodes as keys and closeness vitality as the | |
| value. Otherwise, it returns only the closeness vitality for the | |
| specified `node`. | |
| The closeness vitality of a node may be negative infinity if | |
| removing that node would disconnect the graph. | |
| Examples | |
| -------- | |
| >>> G = nx.cycle_graph(3) | |
| >>> nx.closeness_vitality(G) | |
| {0: 2.0, 1: 2.0, 2: 2.0} | |
| See Also | |
| -------- | |
| closeness_centrality | |
| References | |
| ---------- | |
| .. [1] Ulrik Brandes, Thomas Erlebach (eds.). | |
| *Network Analysis: Methodological Foundations*. | |
| Springer, 2005. | |
| <http://books.google.com/books?id=TTNhSm7HYrIC> | |
| """ | |
| if wiener_index is None: | |
| wiener_index = nx.wiener_index(G, weight=weight) | |
| if node is not None: | |
| after = nx.wiener_index(G.subgraph(set(G) - {node}), weight=weight) | |
| return wiener_index - after | |
| vitality = partial(closeness_vitality, G, weight=weight, wiener_index=wiener_index) | |
| # TODO This can be trivially parallelized. | |
| return {v: vitality(node=v) for v in G} | |