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I am interested in understanding a scientific article to replicate its results. My background is not mathematics or physics, but I am interested to implement a program to compute what the article describe.

Ref: https://doi.org/10.1007/s10955-018-2076-z

Could you help to clarify how to solve this system of equations ? First time I met a lagrangian multiplier, I understood it indicate local min / max in constraints functions.

I would like to understand passage to solve systems of equations (could be done in Mathematica symbolic language) but post here to understand the concept.

The paper describes the following (See Methods):

  1. Given a network A, It describe the degree of a node i as the sum of the probability p that node i is connected to a node j . xi, xj are the lagrangian multipliers that describe probability that edge exist, given the degree of node i

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  1. The paper propose to solve a system of equations, where the sum of the probabilities is equivalent to the degree of node i: below you see the list of probabilities for all possible edges between node i and the other n nodes in network A

enter image description here

  1. Now, the key point for solving the system of equations, is to obtain the coefficient probability for nodes i {qjk} (see point (5) in paper).

I start to be confused with the notation: I understood q reflect the probability that a node i is connected with j with a certain degree k.

enter image description here

The passage to solve the system of equation above, is here:

The problem of quantifying the informativeness of the ego-network of each node can, in fact, be restated by imagining that the node itself is removed from the network. In this way, a reduced adjacency matrix remains naturally defined, inducing, in turn, a reduced system of equations.

Could you help in clarify how to solve the system of equations, and how to find q coefficients ? How can I do, if I don't know what lagrange multipliers are ?

It will be of help if show me the passage, especially on the last one: my purpose is implement a program to do that, and replicate results of the paper.

Thank you already for your help!

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