Numerical & Statistical Analysis about RNGs(Relative Neighbor Graphs) living on a spherical surface
- Project Overview
- Introduction
- Justification
- Goals
- Hypothesis
- Metodology
- Libreries
- Packages
- Results
- Conclusions
- References
This project aims to understand, explore, and characterize the different numerical, geometric, and algebraic properties and relationships that exist when computationally constructing a family of RNG graphs on the surface of a sphere.
Estudiar grafos de vecindad relativa (RNG, Relative Neighborhood Graphs) sobre la superficie de la esfera unitaria y proponer modelos aproximados de RNG por medio de gráficas random.
1.1 Extraer las propiedades estadísticas relevantes de las gráficas RNG
1.2 Relacionar las propiedades de las RNG con la superficie del grafo.
1.3 Implementar una definición de entropía como área dentro de la cual puede moverse los vértices de las gráficas RNG sin afectar su matriz de adyacencia
1.4 Proponer un modelo que genere grafos random que aproxime una RNG utilizando nuestros resultados del análisis estadístico en forma de heurísticas (distribución de número de links y distribución del valor de distancia de links).
Draft the final results of the sensitivity analyses.
The term "RNG" stands for "Relative Network Graph."
The development of a model for generating random graphs that approximate RNGs is a key objective, as it will allow for further analysis and exploration of these networks.
The perturbation and analysis of node positions will provide insights into the available area for node placement and the overall structure of RNGs.
The proposal of a new entropy definition for RNG graphs is an innovative contribution to the field of network science.
The final results of the sensitivity analyses will provide valuable information about the impact of different parameters on the behavior of RNGs.
As the first step in a series of reports, we analyzed the data from the results obtained generated ,the results are presented in the paper titled "Relative Neighbourhood Graphs on the sphere", which provides the record of the relative frequencies representing the probability that the length of an edge generated in an RNG graph falls within a range of values (it is a range and not specific values because it is working in the continuous and in continuous probability, intervals are used).
These distances are then grouped into specific intervals within a range of 0 to pi, divided into 400 equal-sized intervals. The results indicated a non-uniform distribution of edges along the sphere and a relationship between the geodesic distance and the relative frequency of edge occurrence. In general, this study (report) presents the results obtained from the descriptive statistical analysis conducted on the geometric structure of the graphs on the surface of a sphere when they are randomly generated with a uniform distribution of points along with a criterion that we will explain later, which determines whether there is a connection link between two nodes
- Pandas version 1.4.1
- Matplotlib version 3.2.2
- Numpy version 1.21.5
- Numba_____version_0.58.1
- Scipy_____version_1.11.4
- itertools
- time
- copy
- Jupyter lab 3.2.9
├── LICENSE
├── Makefile <- Makefile with commands like `make data` or `make train`
├── README.md <- The top-level README for developers using this project.
├── data
│ ├── external <- Data from third party sources.
│ ├── interim <- Intermediate data that has been transformed.
│ ├── processed <- The final, canonical data sets for modeling.
│ └── raw <- The original, immutable data dump.
│
├── docs <- A default Sphinx project; see sphinx-doc.org for details
│
├── models <- Trained and serialized models, model predictions, or model summaries
│
├── notebooks <- Jupyter notebooks. Naming convention is a number (for ordering),
│ the creator's initials, and a short `-` delimited description, e.g.
│ `1.0-jqp-initial-data-exploration`.
│
├── references <- Data dictionaries, manuals, and all other explanatory materials.
│
├── reports <- Generated analysis as HTML, PDF, LaTeX, etc.
│ └── figures <- Generated graphics and figures to be used in reporting
│
├── requirements.txt <- The requirements file for reproducing the analysis environment, e.g.
│ generated with `pip freeze > requirements.txt`
│
├── setup.py <- makes project pip installable (pip install -e .) so src can be imported
├── src <- Source code for use in this project.
│ ├── __init__.py <- Makes src a Python module
│ │
│ ├── data <- Scripts to download or generate data
│ │ └── make_dataset.py
│ │
│ ├── features <- Scripts to turn raw data into features for modeling
│ │ └── build_features.py
│ │
│ ├── models <- Scripts to train models and then use trained models to make
│ │ │ predictions
│ │ ├── predict_model.py
│ │ └── train_model.py
│ │
│ └── visualization <- Scripts to create exploratory and results oriented visualizations
│ └── visualize.py
│
└── tox.ini <- tox file with settings for running tox; see tox.readthedocs.io
This dataset contains information about different graphs. For each graph, its unique identifier, list of nodes and list of edges, as well as descriptive statistics and details about each node and edge, are recorded.
The data was obtained through a graph generation simulation.
The dataset contains information on 1000 different graphs.
grafo.id: Identificador único del grafo (int).
grafo.lista_nodos: Lista de identificadores únicos de los nodos que conforman el grafo (list).
grafo.lista_aristas: Lista de identificadores únicos de las aristas que conforman el grafo (list).
grafo.estadisticas.num_nodos: Número de nodos que conforman el grafo (int).
grafo.estadisticas.num_aristas: Número de aristas que conforman el grafo (int).
grafo.estadisticas.grado_maximo: Grado máximo de los nodos del grafo (int).
grafo.estadisticas.grado_minimo: Grado mínimo de los nodos del grafo (int).
grafo.estadisticas.grado_promedio: Grado promedio de los nodos del grafo (float).
grafo.estadisticas.densidad: Densidad del grafo (float).
nodos.id: Identificador único del nodo (int).
nodos.coordenada_x: Coordenada en el eje X del nodo (float).
nodos.coordenada_y: Coordenada en el eje Y del nodo (float).
aristas.id: Identificador único de la arista (int).
aristas.nodo_inicial: Identificador único del nodo inicial de la arista (int).
aristas.nodo_final: Identificador único del nodo final de la arista (int).
aristas.distancia: Distancia entre los nodos inicial y final de la arista (float).
aristas.angulo_1: Ángulo de la arista respecto al eje X (float o null).
aristas.angulo_2: Ángulo de la arista respecto al eje Y (float o null).
grafo.id: int
grafo.lista_nodos: list
grafo.lista_aristas: list
grafo.estadisticas.num_nodos: int
grafo.estadisticas.num_aristas: int
grafo.estadisticas.grado_maximo: int
grafo.estadisticas.grado_minimo: int
grafo.estadisticas.grado_promedio: float
grafo.estadisticas.densidad: float
nodos.id: int
nodos.coordenada_x: float
nodos.coordenada_y: float
aristas.id: int
aristas.nodo_inicial: int
aristas.nodo_final: int
aristas.distancia: float
aristas.angulo_1: float o null
aristas.angulo_2: float o null
Los valores faltantes en el dataset se indicarán con el valor NaN para las columnas numéricas
{
"grafo": {
"id": 1,
"lista_nodos": [1, 2, 3, 4, 5],
"lista_aristas": [1, 2, 3, 4],
"estadisticas": {
"num_nodos": 5,
"num_aristas": 4,
"grado_maximo": 2,
"grado_minimo": 1,
"grado_promedio": 1.6,
"densidad": 0.4
}
},
"nodos": [
{
"id": 1,
"coordenada_x": 0.0,
"coordenada_y": 1.0
},
{
"id": 2,
"coordenada_x": 1.0,
"coordenada_y": 0.0
},
{
"id": 3,
"coordenada_x": -1.0,
"coordenada_y": 0.0
},
{
"id": 4,
"coordenada_x": 0.0,
"coordenada_y": -1.0
},
{
"id": 5,
"coordenada_x": 0.5,
"coordenada_y": 0.5
}
],
"aristas": [
{
"id": 1,
"nodo_inicial": 1,
"nodo_final": 2,
"distancia": 1.41421356,
"angulo_1": null,
"angulo_2": null
},
{
"id": 2,
"nodo_inicial": 1,
"nodo_final": 3,
"distancia": 1.41421356,
"angulo_1": null,
"angulo_2": null
},
{
"id": 3,
"nodo_inicial": 1,
"nodo_final": 5,
"distancia": 1.11803399,
"angulo_1": null,
"angulo_2": null
},
{
"id": 4,
"nodo_inicial": 2,
"nodo_final": 3,
"distancia": 2.0,
"angulo_1": null,
"angulo_2": null
}
]
}