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## Project description

DenGraph performs a density-based graph clustering. The algorithm was proposed as an extension for DBSCAN to support overlapping clusters. The approach is based around the neighbourhood of a node. The neighbourhood is defined by the number of reachable nodes within a given distance. Therefore, large groups of items which are close to each other form clusters. As DenGraph is a non-partitioning approach, isolated, distinct and uncommon items are left unclustered. Instead, they are treated as noise.

## Quick Overview

To use dengraph for clustering your data, two steps are required:

• Your data must be provided via the dengraph.graph.Graph interface. See the dengraph.graphs module for appropriate containers and examples.

• The graph must be fed to dengraph.dengraph.DenGraphIO.

>>> from dengraph.graphs.distance_graph import DistanceGraph
>>> from dengraph.dengraph import DenGraphIO
>>> # Graph with defined nodes, edges from distance function
>>> graph = DistanceGraph(
...     nodes=(1, 2, 3, 4, 5, 10, 11, 13, 14, 15, 17, 22, 23, 24, 25, 28, 29, 30, 31),
...     distance=lambda node_from, node_to: abs(node_from - node_to)
... )
>>> # Cluster the graph
>>> clustered_data = DenGraphIO(graph, cluster_distance=2, core_neighbours=3).clusters
>>> # And print clusters
>>> for cluster in sorted(clustered_data, key=lambda clstr: min(clstr)):
...     print(sorted(cluster))
[1, 2, 3, 4, 5]
[11, 13, 14, 15, 17]
[22, 23, 24, 25]
[28, 29, 30, 31]

## Further Information

At the moment, you must refer to the module and class documentation.

• See dengraph.dengraph.DenGraphIO for an explanation of clustering settings.

• See dengraph.graph.Graph for documentation of the graph interface.

### Useful Classes

We provide several implementations and tools for the Graph interface:

• Create a graph from a list of nodes and a distance function via dengraph.graphs.distance_graph.DistanceGraph

• Why is there no DenGraphHO class?

We haven’t implemented that one yet. It’s on our Todo.

• Why is there no DenGraph class?

The original DenGraph algorithm is non-deterministic for unordered graphs. Since border nodes can belong to only one cluster, the first cluster wins - results depend on iteration order. The DenGraphIO algorithm does not have this issue and performs equally well.

• Why is DenGraphO the same class as DenGraphIO?

Algorithmically, DenGraphIO is basically DenGraphO plus the option to insert/remove/modify nodes/edges. In the static case (just initialisation), both are equivalent. At the moment, we don’t have any optimisations based on immutability of DenGraphO. The alias exists so that applications can distinguish between the two, possibly benefiting from future optimisations.

## Acknowledgement

This module is based on several publications:

• [1] T. Falkowski, A. Barth, and M. Spiliopoulou, “DENGRAPH: A Density-based Community Detection Algorithm,” presented at the IEEE/WIC/ACM International Conference on Web Intelligence (WI’07), 2007, pp. 112–115.

• [2] T. Falkowski, A. Barth, and M. Spiliopoulou, “Studying community dynamics with an incremental graph mining algorithm,” AMCIS 2008 Proceedings, 2008.

• [3] N. Schlitter, T. Falkowski, and J. Lässig, “DenGraph-HO - a density-based hierarchical graph clustering algorithm.,” Expert Systems, vol. 31, no. 5, pp. 469–479, 2014.

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