From a86962cbfd0321387c920a04188512d0de2f3036 Mon Sep 17 00:00:00 2001 From: KatolaZ Date: Mon, 19 Oct 2015 16:30:12 +0100 Subject: First commit of MAMMULT documentation --- doc/html/mammult_docsu33.html | 233 ++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 233 insertions(+) create mode 100644 doc/html/mammult_docsu33.html (limited to 'doc/html/mammult_docsu33.html') diff --git a/doc/html/mammult_docsu33.html b/doc/html/mammult_docsu33.html new file mode 100644 index 0000000..d9b78dd --- /dev/null +++ b/doc/html/mammult_docsu33.html @@ -0,0 +1,233 @@ + + +1.2.3.0 knn_q_from_layers.py + + + + + + + + +

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knn_q_from_layers.py
+

NAME +

knn_q_from_layers.py - compute intra-layer and inter-layer degree-degree +correlation coefficients. +

SYNOPSYS +

knn_q_from_layers.py <layer1> <layer2> +

DESCRIPTION +

Compute the intra-layer and the inter-layer degree correlation functions for +two layers given as input. The intra-layer degree correlation function quantifies +the presence of degree-degree correlations in a single layer network, and is defined +as: +
+
+ --1- ∑ ′ ′ +⟨knn(k)⟩ = kNk k P(k |k ) + k′ +
+

+

where P(k′|k) is the probability that a neighbour of a node with degree k has +degree k′, and Nk is the number of nodes with degree k. The quantity ⟨knn(k)⟩ is +the average degree of the neighbours of nodes having degree equal to +k. +

If we consider two layers of a multiplex, and we denote by k the degree +of a node on the first layer and by q the degree of the same node on +the second layers, the inter-layer degree correlation function is defined +as +
+ + + +
+-- ∑ ′ ′ +k(q) = k P(k |q) + k′ +
+

+

where P(k′|q) is the probability that a node with degree q on the second layer +has degree equal to k′ on the first layer, and Nq is the number of nodes +with degree q on the second layer. The quantity k(q) is the expected +degree at layer 1 of node that have degree equal to q on layer 2. The dual +quantity: +
+
+-- ∑ ′ ′ +q(k) = q P(q |k) + q′ +
+

+

is the average degree on layer 2 of nodes having degree k on layer +1. +

OUTPUT +

The program creates two output files, respectively called +

  file1_file2_k1 +

and +

  file1_file2_k2 +

The first file contains a list of lines in the format: +

  k ⟨knn(k)⟩ σk q(k) σq +

where k is the degree at first layer, ⟨knn(k)⟩ is the average degree of the +neighbours at layer 1 of nodes having degree k at layer 1, σk is the standard +deviation associated to ⟨knn(k)⟩, q(k) is the average degree at layer 2 of nodes + + + +having degree equal to k at layer 1, and σq is the standard deviation associated +to q(k). +

The second file contains a similar list of lines, in the format: +

  q ⟨qnn(q)⟩ σq k(q) σk +

with obvious meaning. +

REFERENCE +

V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, Phys. Rev. E 92, 032805 (2015). +

Link to paper: http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805 +

V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex +networks”, Phys. Rev. Lett. 111, 058701 (2013). +

Link to paper: http://prl.aps.org/abstract/PRL/v111/i5/e058701 +

V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Non-linear growth and +condensation in multiplex networks”, Phys. Rev. E 90, 042807 (2014). +

Link to paper: http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807 + + + +

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