Commit 083a4d64 authored by Tiago Peixoto's avatar Tiago Peixoto

Fix path weights in absolute_trust()

This fixes how paths are weighted in the absolute_trust algorithm.
parent e3c6b395
......@@ -29,7 +29,7 @@ using namespace boost;
using namespace graph_tool;
void absolute_trust(GraphInterface& g, int64_t source, boost::any c,
boost::any t, size_t n_paths, double epsilon, bool reversed)
boost::any t, size_t n_paths, bool reversed)
if (!belongs<edge_floating_properties>()(c))
throw ValueException("edge property must be of floating point value type");
......@@ -38,7 +38,8 @@ void absolute_trust(GraphInterface& g, int64_t source, boost::any c,
bind<void>(get_absolute_trust(), _1, g.GetVertexIndex(),
source, _2, _3, n_paths, epsilon, reversed),
g.GetEdgeIndex(), g.GetMaxEdgeIndex(),
source, _2, _3, n_paths, reversed),
vertex_floating_vector_properties())(c, t);
......@@ -48,60 +48,91 @@ struct path_cmp
typedef bool result_type;
inline bool operator()(size_t a, size_t b)
if (get<0>(_paths[a]).first == get<0>(_paths[b]).first)
if (get<0>(_paths[a]).second == get<0>(_paths[b]).second)
return get<1>(_paths[a]).size() > get<1>(_paths[b]).size();
return get<0>(_paths[a]).first < get<0>(_paths[b]).first;
return get<0>(_paths[a]).second < get<0>(_paths[b]).second;
struct get_absolute_trust
template <class Graph, class VertexIndex, class TrustMap,
template <class Graph, class VertexIndex, class EdgeIndex, class TrustMap,
class InferredTrustMap>
void operator()(Graph& g, VertexIndex vertex_index, int64_t source,
TrustMap c, InferredTrustMap t, size_t n_paths,
double epsilon, bool reversed) const
void operator()(Graph& g, VertexIndex vertex_index, EdgeIndex edge_index,
size_t max_edge_index, int64_t source, TrustMap c,
InferredTrustMap t, size_t n_paths, bool reversed) const
typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;
typedef typename graph_traits<Graph>::edge_descriptor edge_t;
typedef typename property_traits<TrustMap>::value_type c_type;
typedef typename property_traits<InferredTrustMap>::value_type
::value_type t_type;
typedef typename property_traits<InferredTrustMap>::value_type::
value_type t_type;
// the path type: the first value is the (trust,weight) pair, the second
// the set of vertices in the path and the third is the list of edges,
// in the path sequence.
typedef tuple<pair<t_type, t_type>, tr1::unordered_set<vertex_t>,
size_t > path_t;
vector<edge_t> > path_t;
double delta = epsilon+1;
int i, N = num_vertices(g);
int i, N = (source == -1) ? num_vertices(g) : source + 1;
#pragma omp parallel for default(shared) private(i) schedule(dynamic)
for (i = (source == -1) ? 0 : source;
i < ((source == -1) ? N : source + 1); ++i)
for (i= (source == -1) ? 0 : source; i < N; ++i)
vertex_t v = vertex(i, g);
if (v == graph_traits<Graph>::null_vertex())
// path priority queue
vector<path_t> paths(1);
vector<size_t> free_indexes;
typedef double_priority_queue<size_t, path_cmp<path_t> > queue_t;
queue_t queue = queue_t(path_cmp<path_t>(paths));
get<0>(paths.back()).first = get<0>(paths.back()).second = 1;
get<2>(paths.back()) = vertex_index[v];
unchecked_vector_property_map<t_type, VertexIndex>
sum_weight(vertex_index, num_vertices(g));
// this is the actual queue of paths which will be used to compute
// the trust values
queue_t final_queue = queue_t(path_cmp<path_t>(paths));
// store all paths which reach a given vertex
path_map(vertex_index, num_vertices(g));
size_t count = 1;
while (!queue.empty())
size_t pi =;
vertex_t w = vertex(get<2>(paths[pi]), g);
vertex_t w;
// push queue top into final queue
if (get<2>(paths[pi]).size() > 0)
w = target(get<2>(paths[pi]).back(), g);
// augment path map
w = v; // the first path
// if maximum size is reached, remove the bottom
if ((n_paths > 0) && (final_queue.size() > n_paths))
size_t bi = final_queue.bottom();
// remove path from path map
if (bi == pi)
// augment paths and put them in the queue
typename graph_traits<Graph>::out_edge_iterator e, e_end;
for (tie(e, e_end) = out_edges(w, g); e != e_end; ++e)
......@@ -109,29 +140,22 @@ struct get_absolute_trust
// no loops
if (get<1>(paths[pi]).find(a) == get<1>(paths[pi]).end())
// new path; only follow non-zero paths
t_type old = (sum_weight[a] > 0) ?
t[v][a]/sum_weight[a] : 0;
// only follow non-zero paths
if (c[*e] > 0 || (reversed &&
get<1>(paths[pi]).size() == 1))
size_t npi;
if (free_indexes.empty())
paths.push_back(paths[pi]); // clone last path
npi = paths.size()-1;
npi = free_indexes.back();
paths[npi] = paths[pi];
paths.push_back(paths[pi]); // clone last path
npi = paths.size()-1;
path_t& np = paths[npi]; // new path
path_t& np = paths[npi];
if (!reversed)
// path weight
get<0>(np).second = get<0>(np).first;
// path value
get<0>(np).first *= c[*e];
......@@ -141,46 +165,131 @@ struct get_absolute_trust
get<0>(np).first *= c[*e];
get<2>(np) = vertex_index[a];
t[v][a] += get<0>(np).first*get<0>(np).second;
sum_weight[a] += get<0>(np).second;
if (n_paths > 0 && queue.size() > n_paths)
size_t bi = queue.bottom();
// keep following paths only if there is a chance
// they will make it into the final queue
if ((n_paths > 0 && final_queue.size() < n_paths) ||
(final_queue.size() == 0 ||
(get<0>(np).second >=
unchecked_vector_property_map<t_type, VertexIndex>
weight_sum(vertex_index, num_vertices(g));
// paths which were already calculated and can be skipped
tr1::unordered_set<size_t> skip;
// calculate trust from paths in the final queue
while (!final_queue.empty())
size_t pi =;
path_t& p = paths[pi];
if (skip.find(pi) != skip.end())
// mark edges which are to be considered
unchecked_vector_property_map<uint8_t, EdgeIndex>
mark(edge_index, max_edge_index+1);
tr1::unordered_set<size_t>& apaths =
path_map[target(get<2>(p).back(), g)]; // all paths with the
// same final target
tr1::unordered_set<size_t> vlist; // all vertices involved
for (typeof(apaths.begin()) iter = apaths.begin();
iter != apaths.end(); ++iter)
for (size_t j = 0; j < get<2>(paths[*iter]).size(); ++j)
edge_t e = get<2>(paths[*iter])[j];
mark[e] = 1;
// compute out trust
unchecked_vector_property_map<t_type, VertexIndex>
out_trust(vertex_index, num_vertices(g));
for (typeof(vlist.begin()) viter = vlist.begin();
viter != vlist.end(); ++viter)
vertex_t u = *viter;
if (!reversed)
typename graph_traits<Graph>::out_edge_iterator e,e_end;
for (tie(e, e_end) = out_edges(u, g); e != e_end; ++e)
if (mark[*e] == 1)
out_trust[u] += c[*e];
// if reversed, use "in-trust" instead
typename in_edge_iteratorS<Graph>::type e, e_end;
for (tie(e, e_end) =
in_edge_iteratorS<Graph>::get_edges(v, g);
e != e_end; ++e)
sum_weight[a] += get<0>(paths[pi]).first;
if (mark[*e] == 1)
out_trust[u] += c[*e];
if (sum_weight[a] > 0)
delta += abs(old-t[v][a]/sum_weight[a]);
if ((count % N) == 0)
for (typeof(apaths.begin()) iter = apaths.begin();
iter != apaths.end(); ++iter)
if (delta < epsilon)
delta = 0;
size_t pi = *iter;
path_t& p = paths[pi];
// calculate the trust value and weight of the path
t_type w = 1, val = 1;
for (size_t i = 0; i < get<2>(p).size(); ++i)
edge_t e = get<2>(p)[i];
vertex_t u = (!reversed) ?
boost::source(e,g) : target(e,g);
if (out_trust[u] > 0)
if ((!reversed && i < get<2>(p).size()-1) ||
(reversed && i > 0))
w *= c[e]*c[e]/out_trust[u];
w *= c[e]/out_trust[u];
val *= c[e];
vertex_t u = target(get<2>(p).back(), g);
weight_sum[u] += w;
t[v][u] += w*val;
typename graph_traits<Graph>::vertex_iterator w, w_end;
for (tie(w, w_end) = vertices(g); w != w_end; ++w)
int j, N = num_vertices(g);
#pragma omp parallel for default(shared) private(j) \
for (j = 0; j < N; ++j)
if (sum_weight[*w] > 0)
t[v][*w] /= sum_weight[*w];
vertex_t w = vertex(i, g);
if (w == graph_traits<Graph>::null_vertex())
if (weight_sum[w] > 0)
t[v][w] /= weight_sum[v];
......@@ -57,7 +57,6 @@ public:
void pop_bottom()
swap(_queue.front(), _queue.back());
if (!_queue.empty())
......@@ -406,11 +406,11 @@ def eigentrust(g, trust_map, vprop=None, norm=False, epslon=1e-6, max_iter=0,
return vprop
def absolute_trust(g, trust_map, source=None, vprop=None, epsilon=1e-6,
n_paths=100000, reversed=False):
def absolute_trust(g, trust_map, source = None, vprop=None, n_paths=10000,
Calculate the absolute trust centrality of each vertex in the graph, or only
for a given source, if one is provided.
Calculate the absolute trust centrality of each vertex in the graph, from a
given source.
......@@ -419,16 +419,14 @@ def absolute_trust(g, trust_map, source=None, vprop=None, epsilon=1e-6,
trust_map : :class:`~graph_tool.PropertyMap`
Edge property map with the values of trust associated with each
edge. The values must lie in the range [0,1].
source : Vertex, optional (default: None)
A vertex which is used the as the sole source for gathering trust
values, instead of all the vertices in the graph.
source : Vertex (optional, default: None)
A vertex which is used the as the source for gathering trust values. If
left unspecified, the trust values for all sources are computed.
vprop : :class:`~graph_tool.PropertyMap`, optional (default: None)
Vertex property map where the values of eigentrust must be stored.
epsilon : float, optional (default: 1e-6)
Convergence criterion for the algorithm. If the summed difference of
trust values drops below this value, the algorithm stops.
n_paths : int, optimal (default: 100000)
Maximum number of paths to keep following at any given time.
Vector vertex property map where the values of trust for each source
must be stored.
n_paths : int, optimal (default: 10000)
Maximum number of paths to consider.
reversed : bool, optional (default: False)
Calculates the "reversed" trust instead: The direction of the edges are
inverted, but the path weighting is preserved in the original direction
......@@ -466,15 +464,19 @@ def absolute_trust(g, trust_map, source=None, vprop=None, epsilon=1e-6,
.. math::
w_{\{i\to j\}} = \prod_{e\in \{i\to j\}}\{\delta_{t(e),j}(1-c_e) + c_e\},
w_{\{i\to j\}} = \prod_{e\in \{i\to j\}}\frac{c_e}{\Gamma^+_{\{i\to j\}}(s(e))}
\{c_e(1-\delta_{t(e),j}) + \delta_{t(e),j}},
such that the direct trust of the last edge on the path is not considered.
such that the direct trust of the last edge on the path is not
considered. The value :math:`\Gamma^+_{\{i\to j\}}(s(e))` is the sum of
trust values of the selected out-edges of vertex :math:`s(e)`, which also
belong to the set of edge-disjoint of paths from i to j.
The algorithm measures the absolute trust by following all vertex-disjoint
paths, and keeping them on a priority queue. Each iteration the path with
maximum weight is augmented, and the new paths pushed into the queue. The
algorithm stops when all paths are consumed, or when the trust values are
not making any progress, according to the epsilon parameter.
algorithm stops when all paths are consumed, or when the all the ``n_paths``
paths with largest weights are found.
If enabled during compilation, this algorithm runs in parallel.
......@@ -487,31 +489,31 @@ def absolute_trust(g, trust_map, source=None, vprop=None, epsilon=1e-6,
>>> trust.get_array()[:] = random(g.num_edges())
>>> t = gt.absolute_trust(g, trust, source=g.vertex(0))
>>> print t.a
[ 0.00000000e+00 5.14258135e-02 5.71266121e-03 5.72445966e-04
0.00000000e+00 8.40870736e-03 5.26183548e-03 1.17886060e-03
6.01506397e-04 1.29831325e-03 1.45797971e-03 3.21480292e-04
1.71096778e-03 2.74688614e-03 4.62071739e-03 8.09703326e-04
0.00000000e+00 2.32699564e-03 1.26410922e-03 2.39985303e-03
5.82052160e-03 2.76647806e-03 6.63350769e-03 2.20195841e-03
1.29581958e-04 5.18096899e-03 1.92592209e-03 1.81210154e-03
1.45646324e-03 3.43043712e-03 2.45289182e-02 4.32648258e-03
9.89190855e-04 1.45417521e-03 0.00000000e+00 9.99423350e-04
7.88399750e-05 0.00000000e+00 3.03832976e-03 8.55065176e-03
0.00000000e+00 4.55137037e-03 3.81341021e-03 1.19730767e-03
7.18323777e-04 4.09318494e-03 4.00794452e-04 1.09034564e-02
9.79985323e-04 1.33199924e-03 3.50390276e-03 9.94522820e-04
1.58366908e-03 1.67022801e-03 2.66247928e-03 9.99978606e-04
5.60094151e-03 1.75052181e-03 4.69095413e-03 4.66550013e-04
1.61261048e-03 4.64164507e-03 1.29879335e-02 1.21931927e-03
1.03114062e-03 2.38873202e-01 4.40785917e-03 2.05076506e-03
1.67546702e-03 1.24570365e-01 0.00000000e+00 5.72146010e-04
2.44438711e-03 2.92452098e-03 2.12275007e-04 7.39329792e-04
2.62264044e-01 3.34209850e-04 1.37313498e-03 1.54652980e-03
3.93973002e-04 5.35530090e-04 7.35038003e-04 1.89651401e-03
5.90688369e-03 2.40109219e-03 1.98770683e-03 1.13007595e-04
6.62879127e-03 2.50902780e-02 2.25743105e-03 3.42120043e-03
4.94039204e-04 5.57933981e-03 2.84245886e-03 2.50370261e-03
9.67803400e-03 8.03776616e-02 1.31993888e-03 2.41471529e-03]
[ 0.00000000e+00 5.14258135e-02 2.42874582e-04 1.05347472e-06
0.00000000e+00 3.13429149e-04 1.53697222e-04 3.83063399e-05
2.65668937e-06 2.04029901e-05 1.19582153e-05 2.67743821e-06
1.50606560e-04 1.51595650e-05 5.72684475e-05 2.16466381e-06
0.00000000e+00 4.08340061e-05 3.26896572e-06 7.80860267e-05
7.31033290e-05 7.81690832e-05 2.93440658e-04 1.19013202e-05
1.60601849e-06 6.79167712e-05 9.35414301e-05 1.98991248e-05
2.08142130e-05 1.28565785e-04 2.83893891e-03 8.45362053e-05
1.15751883e-05 1.97248846e-05 0.00000000e+00 7.51004486e-06
5.49704676e-07 0.00000000e+00 1.06219388e-04 9.64852468e-04
0.00000000e+00 4.70496027e-05 5.49108602e-05 6.23617670e-06
1.32625806e-06 7.35202433e-05 2.09546902e-06 1.99138155e-03
4.32934771e-06 2.61887887e-05 2.55099939e-05 3.90874553e-06
9.07765143e-05 2.59243068e-06 7.50032403e-06 8.36211398e-05
7.80814352e-04 8.12133072e-06 6.24066931e-04 2.19465770e-06
4.15039190e-05 5.41464668e-05 1.84421073e-03 8.02449156e-06
4.01472852e-06 3.76746767e-01 7.02886863e-05 1.52365123e-04
4.58687938e-06 3.70470973e-02 0.00000000e+00 1.85922960e-06
2.05481272e-05 1.41021895e-04 1.45217040e-06 3.18562543e-06
2.62264044e-01 7.41140347e-06 1.39150089e-05 3.86583428e-06
2.85681164e-06 4.12923146e-06 7.05705402e-07 2.12584322e-05
1.65948868e-04 3.10144404e-05 5.08749580e-06 0.00000000e+00
1.45435603e-03 4.19224443e-03 4.88198531e-05 3.00152848e-04
5.61591759e-05 2.31951396e-04 1.19051653e-05 2.34710286e-05
6.27636571e-04 1.65759606e-02 1.30944429e-05 1.26282526e-05]
......@@ -538,8 +540,7 @@ def absolute_trust(g, trust_map, source=None, vprop=None, epsilon=1e-6,
get_absolute_trust(g._Graph__graph, source,
_prop("e", g, trust_map),
_prop("v", g, vprop), n_paths, epsilon,
_prop("v", g, vprop), n_paths, reversed)
if reversed:
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