Detecting Core-Periphery Structure in Spatial Networks

This repository hosts the code and some example data for the following paper:

Detecting Core-Periphery Structure in Spatial Networks
Junteng Jia and Austin R. Benson
arXiv:1808.06544, 2018.

Our paper introduce a random network model for networks with core-periphery structure, where each vertex is associated with a real-valued core score to denote its role as a core. A user can do one of the following two things:

• Generate a random network by providing the predefined core score for each vertex.
• Learn core scores of all the vertices by fitting a network to our model. The user need to provide the adjacency matrix, vertex coordinates, metric kernel, and a center-of-mass function under the provided metric kernel.

We have demonstrate in our paper that:

• The learned vertex core scores are useful features for data mining purposes.
• Our algorithms scales to networks with millions of vertices.

Our code is written in Julia 0.6.

Model inference

Given vertex coordinates and network topology, our model infer the vertex core scores by a maximum likelihood estimation. Here is the code snippet for inferencing the vertex core scores for the celegans dataset.

theta, epsilon = SCP_FMM.model_fit(A, coords, Euclidean_CoM2, Euclidean(), epsilon; opt=opt);

Output:

• theta is the vertex core scores.
• epsilon is a parameter in our model that defines the edge length scale.

Input:

• A is the |V| x |V| adjacency matrix of the input network.
• coords is a d x |V| matrix with the vertex coordinates.
• Euclidean_CoM2 is a function that compute the center-of-mass between two vertices.
• Euclidean() is the metric kernel.
• epsilon is the initial value for the length scale parameter.
• opt is a dictionary containing user defined parameters.

Network generation

Given vertex coordinates and vertex core scores, our model sample an instance of random network. Here is the code snippet for generating a random network for celegans dataset.

B = SCP_FMM.model_gen(theta, coords, Euclidean_CoM2, Euclidean(), epsilon; opt=opt);

Output:

• B is the adjacency matrix of the generated random network.

Examples

For a more detailed explanation, please (see examples). For instance, the following code snippet reproduces figure 4 (A) in our paper.

include("examples/celegans_naive.jl");
include("examples/celegans_fmm.jl");
using Plots;

Plots.plot(size=(550,500),-5.0:0.1:1.0,-5.0:0.1:1.0,framestyle=:box,label="ideal",color="red",legend=:topleft);
Plots.scatter!(theta0,theta,label="experiment",color="blue")

If you have any questions, please email to jj585@cornell.edu.