From 91324c91e5c533ec87b48f6b80c64a94bc3e1d0a Mon Sep 17 00:00:00 2001 From: Kerem Keptig <kerem.keptig@stud-mail.uni-wuerzburg.de> Date: Thu, 13 Mar 2025 15:33:16 +0100 Subject: [PATCH] Update 2 files - /TemporalPercolationMeasures/percolationMeasures.png - /Read.me --- Read.me | 129 ++++++++++++++++++ .../percolationMeasures.png | Bin 0 -> 65025 bytes 2 files changed, 129 insertions(+) create mode 100644 Read.me create mode 100644 TemporalPercolationMeasures/percolationMeasures.png diff --git a/Read.me b/Read.me new file mode 100644 index 0000000..e417768 --- /dev/null +++ b/Read.me @@ -0,0 +1,129 @@ +# Temporal Percolation Analysis + +## Overview + +This project provides a simple and effective way to analyze percolation transitions in temporal networks, focusing on three primary components: + +1. **Event-Based Percolation (SE)**: Measures the number of event-graph nodes in the largest connected component. +2. **Node-Based Percolation (SG)**: Counts the number of unique temporal network nodes covered by the component. +3. **Lifetime-Based Percolation (SLT)**: Calculates the duration from the earliest to the latest event within a connected component. + +This method is applied to real-world datasets from Wikipedia, Reddit, and UCI to analyze phase transitions. The project provides users to identify percolation behavior efficiently, which can be useful in fields such as information diffusion, epidemic modeling, and network robustness. + +For a deeper understanding of percolation in temporal networks, refer to the foundational work on weighted event graphs by Mikko Kivelä et al. [(link)](https://doi.org/10.48550/arXiv.1709.05647). + +## Features + +- **Temporal Graph Processing**: Constructs event graphs from temporal edge lists using [pathpyG](https://www.pathpy.net/). +- **Connected Components Analysis**: Identifies connected components in event graphs using pathpyG's built-in algorithms. +- **Percolation Metrics Computation**: Computes event-graph node sizes, underlying graph nodes, and component lifetimes. +- **Critical Threshold Detection**: Determines percolation phase transitions. +- **Data Visualization**: Generates plots for component measures, percolation metrics, and probability distributions. + +## Installation + +Ensure you have the required dependencies installed: + +```bash +pip install numpy pandas matplotlib seaborn torch pathpyG itertools +``` + +## Usage + +### 1. Preprocess Data + +```python +file_path = "wikipedia.csv" +bipartite = True + +df = preprocess(file_path) + +# Normalize timestamps +df['normalized_ts'] = (df['ts'] - df['ts'].min()) +tedges = list(df[['u', 'i', 'normalized_ts']].itertuples(index=False, name=None)) + +# Construct Temporal Graph +temporal_graph = pp.TemporalGraph.from_edge_list(tedges) +total_events = len(tedges) +``` + +### 2. Perform Percolation Analysis + +```python +bipartite_percolation = TemporalPercolation(temporal_graph, total_events) + +delta_t_values = np.linspace(df['normalized_ts'].min(), df['normalized_ts'].max(), 200) +analysis_results, percolation_metrics = bipartite_percolation.percolation_analysis(delta_t_values) +``` + +### 3. Visualize Results + +```python +bipartite_percolation.compare_component_measures(analysis_results) +bipartite_percolation.plot_largest_component(analysis_results, delta_t_values) +``` + +### 4. Compute Order Parameters + +```python +delta_t_values, rho_E, rho_G, rho_LT, chi_E, chi_G, chi_LT, P_S_E_distributions, P_S_LT_distributions, P_S_G_distributions = bipartite_percolation.compute_order_parameters(analysis_results, temporal_graph) +``` + +### 5. Plot Percolation Metrics + +```python +rho_metrics = [rho_E, rho_G, rho_LT] +chi_metrics = [chi_E, chi_G, chi_LT] +labels = [(r'$Ï_E$', r'$χ_E$'), (r'$Ï_G$', r'$χ_G$'), (r'$Ï_{LT}$', r'$χ_{LT}$')] +colors = ('red', 'blue') + +bipartite_percolation.plot_percolation_metrics(delta_t_values, rho_metrics, chi_metrics, labels, colors, time_range=100) +``` + +### 6. Compute Probability Distributions + +```python +selected_delta_t_values = [3.6, 7.2, 25.2] +for dt in selected_delta_t_values: + if dt in P_S_E_distributions: + sizes = np.array(list(P_S_E_distributions[dt].keys())) + probabilities = np.array(list(P_S_E_distributions[dt].values())) + plt.scatter(sizes, probabilities, label=f'$\delta t$ = {dt:.1f} hours') +plt.xscale("log") +plt.yscale("log") +plt.xlabel("$S_E$") +plt.ylabel("$P(S_E)$") +plt.legend() +plt.show() +``` + +## Temporal Percolation Measures + +To better illustrate the different percolation measures used in this analysis, the following diagram visualizes key component metrics: + + + + +- **LCC (Largest Connected Component)**: The primary connected structure in the event graph. +- **SE (Event Graph Nodes)**: Number of event-graph nodes in the largest connected component. +- **SG (Underlying Graph Nodes)**: Number of distinct temporal network nodes covered by the component. +- **SLT (Component Lifetime)**: Difference between the maximum and minimum timestamps of the events in the component. + + +## Citation +The methodology follows the approach introduced by: +``` +@article{kivela2018mapping, + title={Mapping temporal-network percolation to weighted, static event graphs}, + author={Kivel{\"a}, Mikko and Cambe, Jordan and Saram{\"a}ki, Jari and Karsai, M{\'a}rton}, + journal={Scientific reports}, + volume={8}, + number={1}, + pages={12357}, + year={2018}, + publisher={Nature Publishing Group UK London} +} +``` + + + diff --git a/TemporalPercolationMeasures/percolationMeasures.png b/TemporalPercolationMeasures/percolationMeasures.png new file mode 100644 index 0000000000000000000000000000000000000000..7dd5acd30230dd4164f680b2609d37dda492e9cc GIT binary patch literal 65025 zcmd3OWmr{hxAj&OB$e(~N<c!oq>+*a5lIO_36U;?*tAGUC`d`CAR(O!3W799N{7-Z zd~@ORob#UZUDx;f<MO?p7dGs@)_vb|&N0Rua|LUtE8^o&;h<0`{F_R0S}4@HR21q= z!v#$EiKo7oAN=QxvzDR^s<4Y@5xzNREv+VvLX||~9+{no@39?~Zabq;M30gGof)^H 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