Inflow and Outflow Centrality

Python implementation of inflow and outflow centrality — two novel, node-feature-aware centrality metrics inspired by the aggregation approach used in graph convolutional networks (GCNs).

The package also includes two baseline node-weighted metrics — weighted degree centrality and weighted closeness centrality — used in the accompanying paper for comparison.

📄 Paper: Inflow and outflow centrality: novel centrality metrics inspired by graph convolution, published in Applied Network Science. DOI: 10.1007/s41109-026-00782-7

---

Installation

Requires Python ≥ 3.9.

git clone https://github.com/AramPapaz/Inflow-and-Outflow-Centrality.git
cd Inflow-and-Outflow-Centrality
pip install .

This installs the inflow_outflow_centrality package along with its dependencies (pandas, numpy, networkx).

For development (editable install):

pip install -e .

---

Quickstart

As a Python library

from inflow_outflow_centrality import utilities
import pickle

# 1. Load your network
interactions = utilities.read_interactions_csv("example/AirportNetwork.csv")
# or for .ea/.ea.gz files:
# interactions = utilities.read_interactions_ea("example/4efm_intsc.ea")

# 2. Provide node features as a dict {node_id: value}
# (or load real features from your own data)
with open("example/population.pkl", "rb") as f:
    features = pickle.load(f)


# 3. Compute inflow/outflow centrality
result = utilities.flow_metric(interactions, features, flow_type="both")
print(result.head())

# Other available metrics for comparison:
deg_centrality = utilities.node_weighted_degree_centrality(interactions, features)
close_centrality = utilities.node_weighted_closeness_centrality(interactions, features)

From the command line

python -m inflow_outflow_centrality.utilities <flow_type> <interactions_file> [features_csv]

• flow_type — in, out, or both
• interactions_file — network file; .ea/.ea.gz files are parsed with read_interactions_ea, everything else with read_interactions_csv
• features_csv (optional) — 2-column CSV of node_id, feature_value; if omitted, every node defaults to a feature value of 1

The result is written to <flow_type>_output.csv in the same directory as interactions_file.

Example, using the sample data included in this repo:

python -m inflow_outflow_centrality.utilities both example/AirportNetwork.csv

This reproduces example/both_output.csv (comparable to the provided example/inflow_output.csv / example/outflow_output.csv).

---

API Reference

Function	Description
flow_metric(interactions, features, flow_type)	Core inflow/outflow centrality computation. Auto-detects an optional float weight column in interactions and, if present, also returns weight-based versions of the metric (WeightSum, WeightedInflowValue, WeightedOutflowValue).
node_weighted_degree_centrality(interactions, features, f=lambda x: x)	Node-weighted degree centrality baseline. f can transform feature values before aggregation.
node_weighted_closeness_centrality(interactions, features, f=lambda x: x)	Node-weighted closeness centrality baseline.
read_interactions_csv(csv_path)	Loads a CSV edge list into the DataFrame format expected by flow_metric.
read_interactions_ea(ea_path)	Loads a .ea or .ea.gz interaction file, keeping only rows with combi:all_all in the description and non-negative scores.

Input format

• interactions: a pandas.DataFrame with two node-id columns (source, target) and an optional third float column for edge weight. Duplicate and self-interactions are automatically removed.
• features: a dict mapping node_id → feature_value. Values should roughly follow a normal distribution for the metric to behave well. In the example data this is provided as a pickled dict (example/population.pkl), loaded with pickle.load.

Output format

flow_metric returns a pandas.DataFrame:

• flow_type="in" → Node, InflowValue, Degree (+ WeightSum, WeightedInflowValue if weights were provided)
• flow_type="out" → Node, OutflowValue, Degree (+ WeightSum, WeightedOutflowValue if weights were provided)
• flow_type="both" → Node, InflowValue, OutflowValue, Degree (+ weighted columns if weights were provided)

---

Example data

The example/ folder contains ready-to-use sample data:

• AirportNetwork.csv — an airport interaction network
• 4efm_intsc.ea — a residue interaction network in .ea format
• population.pkl — node features (population) for use with the airport network
• inflow_output.csv, outflow_output.csv — precomputed results for reference/comparison