Detect hidden clusters in physical interaction networks fast. Tune iterations, weights, and resolution parameters easily. Export results for reports, simulations, and classroom comparisons anytime.
Paste an edge list and compute communities using label propagation. This method iteratively assigns each node the most common neighbor label.
Copy the example edge list to test the calculator.
| From | To | Weight |
|---|---|---|
| A | B | 1 |
| A | C | 1 |
| B | C | 1 |
| C | D | 1 |
| D | E | 1 |
| D | F | 1 |
| E | F | 1 |
| F | G | 1 |
| G | H | 1 |
| F | H | 1 |
| B | D | 0.2 |
| C | E | 0.2 |
The calculator reports modularity for undirected graphs using a resolution parameter γ. Modularity measures how strongly edges concentrate within detected groups.
The detection step uses label propagation: each node adopts the neighbor label with the greatest total incident weight.
Many physical systems can be modeled as graphs: atoms linked by bonds, oscillators coupled by springs, particles interacting through collisions, or sensors connected by communication edges. Community detection groups nodes that interact more strongly within the group than outside it. This helps reveal modular structure, such as domains, clusters, or functional subsystems.
This tool takes an edge list and returns (a) node-to-community assignments and (b) community-level metrics. The default method is label propagation, an efficient heuristic that typically converges in tens of iterations on sparse networks. For undirected inputs it also reports modularity Q and conductance to summarize separation.
Label propagation starts by giving every node a unique label. During each iteration, a node adopts the label that has the greatest total incident weight among its neighbors. Randomizing the update order can avoid cycling and can produce more stable partitions across runs when a fixed seed is used.
Weights represent interaction strength, similarity, or coupling intensity. A weight of 2 means the connection contributes twice as strongly as a weight of 1 when labels compete. In experimental or simulated data, weights can encode averaged correlations, contact frequency, or measured coupling constants.
Modularity compares observed within-community connectivity to a randomized null model based on node degrees. Typical Q values for meaningful structure often fall between about 0.2 and 0.7, but the scale depends on the network. The resolution parameter γ shifts sensitivity: larger γ tends to split communities into smaller groups.
Conductance measures how much weight exits a community relative to its volume. Lower conductance indicates a tighter community with fewer cross-boundary links. Values near 0 suggest strong separation, while larger values indicate diffuse boundaries or bridge-like structure.
Label propagation runs in roughly linear time with respect to edges per iteration, so it scales well for sparse graphs. For web use, a few thousand edges is typically comfortable. If you increase Max iterations, you may improve convergence, but diminishing returns often appear after 50–100 iterations.
Start with weights if available, set Max iterations to 50, enable randomization, and choose a seed for repeatable outputs. Then adjust γ to explore coarse versus fine partitions. Compare Q, conductance, and membership lists to validate communities against known physical constraints or experimental labels.
Paste one edge per line as “nodeA nodeB weight”. The weight is optional and defaults to 1. You may use spaces or commas, and lines starting with # are ignored.
This page computes modularity using an undirected formulation. If you need modularity, disable the directed option so degrees and internal weights are evaluated consistently with the undirected model.
Use γ = 1 as a baseline. Increase γ to find smaller, more detailed groups; decrease it to merge groups into larger communities. Compare outputs across γ to assess stability.
Low or negative Q suggests the detected grouping is not denser than expected under the null model. This can happen for nearly random graphs, very small networks, or when the chosen γ is unsuitable.
Label propagation can depend on node update order. Enable randomization and set a fixed seed for repeatable results. Different stable label configurations can exist for the same network.
Conductance compares boundary weight to community volume. Lower values indicate tighter separation. If conductance is high, the community has many cross-links and may be better merged or split differently.
Yes. Nodes with no neighbors remain isolated and keep their own label. To include isolated nodes explicitly, ensure they appear in at least one edge line or add a small-weight connection if appropriate.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.