## Mercurial > repos > shellac > sam_consensus_v3

### diff env/lib/python3.9/site-packages/networkx/algorithms/centrality/load.py @ 0:4f3585e2f14b draft default tip

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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"

author | shellac |
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date | Mon, 22 Mar 2021 18:12:50 +0000 |

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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/env/lib/python3.9/site-packages/networkx/algorithms/centrality/load.py Mon Mar 22 18:12:50 2021 +0000 @@ -0,0 +1,197 @@ +"""Load centrality.""" +from operator import itemgetter + +import networkx as nx + +__all__ = ["load_centrality", "edge_load_centrality"] + + +def newman_betweenness_centrality(G, v=None, cutoff=None, normalized=True, weight=None): + """Compute load centrality for nodes. + + The load centrality of a node is the fraction of all shortest + paths that pass through that node. + + Parameters + ---------- + G : graph + A networkx graph. + + normalized : bool, optional (default=True) + If True the betweenness values are normalized by b=b/(n-1)(n-2) where + n is the number of nodes in G. + + weight : None or string, optional (default=None) + If None, edge weights are ignored. + Otherwise holds the name of the edge attribute used as weight. + + cutoff : bool, optional (default=None) + If specified, only consider paths of length <= cutoff. + + Returns + ------- + nodes : dictionary + Dictionary of nodes with centrality as the value. + + See Also + -------- + betweenness_centrality() + + Notes + ----- + Load centrality is slightly different than betweenness. It was originally + introduced by [2]_. For this load algorithm see [1]_. + + References + ---------- + .. [1] Mark E. J. Newman: + Scientific collaboration networks. II. + Shortest paths, weighted networks, and centrality. + Physical Review E 64, 016132, 2001. + http://journals.aps.org/pre/abstract/10.1103/PhysRevE.64.016132 + .. [2] Kwang-Il Goh, Byungnam Kahng and Doochul Kim + Universal behavior of Load Distribution in Scale-Free Networks. + Physical Review Letters 87(27):1–4, 2001. + http://phya.snu.ac.kr/~dkim/PRL87278701.pdf + """ + if v is not None: # only one node + betweenness = 0.0 + for source in G: + ubetween = _node_betweenness(G, source, cutoff, False, weight) + betweenness += ubetween[v] if v in ubetween else 0 + if normalized: + order = G.order() + if order <= 2: + return betweenness # no normalization b=0 for all nodes + betweenness *= 1.0 / ((order - 1) * (order - 2)) + return betweenness + else: + betweenness = {}.fromkeys(G, 0.0) + for source in betweenness: + ubetween = _node_betweenness(G, source, cutoff, False, weight) + for vk in ubetween: + betweenness[vk] += ubetween[vk] + if normalized: + order = G.order() + if order <= 2: + return betweenness # no normalization b=0 for all nodes + scale = 1.0 / ((order - 1) * (order - 2)) + for v in betweenness: + betweenness[v] *= scale + return betweenness # all nodes + + +def _node_betweenness(G, source, cutoff=False, normalized=True, weight=None): + """Node betweenness_centrality helper: + + See betweenness_centrality for what you probably want. + This actually computes "load" and not betweenness. + See https://networkx.lanl.gov/ticket/103 + + This calculates the load of each node for paths from a single source. + (The fraction of number of shortests paths from source that go + through each node.) + + To get the load for a node you need to do all-pairs shortest paths. + + If weight is not None then use Dijkstra for finding shortest paths. + """ + # get the predecessor and path length data + if weight is None: + (pred, length) = nx.predecessor(G, source, cutoff=cutoff, return_seen=True) + else: + (pred, length) = nx.dijkstra_predecessor_and_distance(G, source, cutoff, weight) + + # order the nodes by path length + onodes = [(l, vert) for (vert, l) in length.items()] + onodes.sort() + onodes[:] = [vert for (l, vert) in onodes if l > 0] + + # initialize betweenness + between = {}.fromkeys(length, 1.0) + + while onodes: + v = onodes.pop() + if v in pred: + num_paths = len(pred[v]) # Discount betweenness if more than + for x in pred[v]: # one shortest path. + if x == source: # stop if hit source because all remaining v + break # also have pred[v]==[source] + between[x] += between[v] / float(num_paths) + # remove source + for v in between: + between[v] -= 1 + # rescale to be between 0 and 1 + if normalized: + l = len(between) + if l > 2: + # scale by 1/the number of possible paths + scale = 1.0 / float((l - 1) * (l - 2)) + for v in between: + between[v] *= scale + return between + + +load_centrality = newman_betweenness_centrality + + +def edge_load_centrality(G, cutoff=False): + """Compute edge load. + + WARNING: This concept of edge load has not been analysed + or discussed outside of NetworkX that we know of. + It is based loosely on load_centrality in the sense that + it counts the number of shortest paths which cross each edge. + This function is for demonstration and testing purposes. + + Parameters + ---------- + G : graph + A networkx graph + + cutoff : bool, optional (default=False) + If specified, only consider paths of length <= cutoff. + + Returns + ------- + A dict keyed by edge 2-tuple to the number of shortest paths + which use that edge. Where more than one path is shortest + the count is divided equally among paths. + """ + betweenness = {} + for u, v in G.edges(): + betweenness[(u, v)] = 0.0 + betweenness[(v, u)] = 0.0 + + for source in G: + ubetween = _edge_betweenness(G, source, cutoff=cutoff) + for e, ubetweenv in ubetween.items(): + betweenness[e] += ubetweenv # cumulative total + return betweenness + + +def _edge_betweenness(G, source, nodes=None, cutoff=False): + """Edge betweenness helper.""" + # get the predecessor data + (pred, length) = nx.predecessor(G, source, cutoff=cutoff, return_seen=True) + # order the nodes by path length + onodes = [n for n, d in sorted(length.items(), key=itemgetter(1))] + # initialize betweenness, doesn't account for any edge weights + between = {} + for u, v in G.edges(nodes): + between[(u, v)] = 1.0 + between[(v, u)] = 1.0 + + while onodes: # work through all paths + v = onodes.pop() + if v in pred: + # Discount betweenness if more than one shortest path. + num_paths = len(pred[v]) + for w in pred[v]: + if w in pred: + # Discount betweenness, mult path + num_paths = len(pred[w]) + for x in pred[w]: + between[(w, x)] += between[(v, w)] / num_paths + between[(x, w)] += between[(w, v)] / num_paths + return between