PaperlayerView exact revision on arXiv

Source-linked AI summary

EdMot: An Edge Enhancement Approach for Motif-aware Community Detection

Pei-Zhen Li, Ling Huang, Chang-Dong Wang, Jian-Huang Lai

arXiv:1906.04560v1cs.SIphysics.soc-ph

TL;DR

Many community-detection methods use only node-edge structure, while motif-based methods can encounter fragmented hypergraphs that leave same-community nodes ungrouped. EdMot partitions large hypergraph components into modules and uses edge enhancement to rewire the original network. The authors report improved results over original and traditional higher-order partitioning methods, with a stated limitation that only top-K components are processed.

  • Problem

    Lower-order methods can miss motif-based organization, while motif-based hypergraphs may fragment and leave nodes without hypergraph connections ungrouped despite sharing a community.

    Source: §1 · pp. 1–2, §2 · p. 2

  • Method

    EdMot partitions the top K largest motif-hypergraph components into modules, derives cliques from them through edge enhancement, and partitions the rewired original network.

    Source: §1 · p. 2, §3.1 · p. 3, §3.2 · p. 4

  • Results

    About 17% NMI improvement over Louvain and 14% over Motif-Louvain on average; EdMot-Louvain achieves the best NMI, F-score, and modularity on polbooks, polblogs, and Cora.

    Source: §4.3 · p. 6

  • Takeaways & Limitations

    The reported results indicate EdMot can outperform original graph partitioning and traditional higher-order methods, and may improve some state-of-the-art graph partitioners even without fragmentation.

    Source: §4.3 · p. 6

    Only the top K largest hypergraph components are processed, so the resulting module set includes only part of the network’s nodes.

    Source: §3.3 · p. 4

Abstract

from arXiv · show

Network community detection is a hot research topic in network analysis. Although many methods have been proposed for community detection, most of them only take into consideration the lower-order structure of the network at the level of individual nodes and edges. Thus, they fail to capture the higher-order characteristics at the level of small dense subgraph patterns, e.g., motifs. Recently, some higher-order methods have been developed but they typically focus on the motif-based hypergraph which is assumed to be a connected graph. However, such assumption cannot be ensured in some real-world networks. In particular, the hypergraph may become fragmented. That is, it may consist of a large number of connected components and isolated nodes, despite the fact that the original network is a connected graph. Therefore, the existing higher-order methods would suffer seriously from the above fragmentation issue, since in these approaches, nodes without connection in hypergraph can't be grouped together even if they belong to the same community. To address the above fragmentation issue, we propose an Edge enhancement approach for Motif-aware community detection (EdMot). The main idea is as follows. Firstly, a motif-based hypergraph is constructed and the top K largest connected components in the hypergraph are partitioned into modules. Afterwards, the connectivity structure within each module is strengthened by constructing an edge set to derive a clique from each module. Based on the new edge set, the original connectivity structure of the input network is enhanced to generate a rewired network, whereby the motif-based higher-order structure is leveraged and the hypergraph fragmentation issue is well addressed. Finally, the rewired network is partitioned to obtain the higher-order community structure.

1 INTRODUCTION

Community detection seeks strongly connected groups, but methods focused on individual nodes and edges can miss motif-based higher-order organization. EdMot addresses fragmentation in motif-based hypergraphs by enhancing connectivity, and the paper reports improved community-detection performance across eight real-world datasets.

1 INTRODUCTION

  • Existing methods focused on individual nodes and edges may fail to capture higher-order network organization, while motif-based methods can underestimate or violate original topology.Fragmentation can leave nodes without hypergraph connections unable to group together even when they belong to the same community.Source: §1 · pp. 1–2
  • EdMot constructs a motif-based hypergraph, partitions its top K largest components into modules, derives a clique from each module, and adds edges to rewire the original network.The rewired network combines motif-based higher-order structure with the original lower-order connectivity before partitioning.Source: §1 · p. 2
  • The paper formalizes hypergraph fragmentation, proposes EdMot to leverage higher-order connections while addressing it, and evaluates the method on eight real-world datasets.The authors report that experiments show EdMot improves community-detection performance over state-of-the-art methods.Source: §1 · p. 2

2 BACKGROUND AND PROBLEM STATEMENT

Motif-based connectivity can differ from the original node-edge structure: nodes may be adjacent in the network yet lack a shared motif. This can fragment the motif hypergraph and leave isolated nodes, motivating EdMot’s edge-enhancement approach.

2 BACKGROUND AND PROBLEM STATEMENT

  • The paper represents a motif with p nodes and q edges, and focuses on the triangle motif while allowing extension to other motifs.The motif adjacency matrix records how many motif instances contain each node pair.Source: §2 · p. 2
  • Motif-based methods preserve higher-order structure but can eliminate edges that occur in no motifs, underestimating or violating the original lower-order structure.The motif adjacency entry for a node pair can be zero even when the original adjacency entry is positive.Source: §2 · p. 2
  • A motif hypergraph built from one connected network component can split into many components and isolated nodes when nodes lack higher-order connections.Figure 1 illustrates this fragmentation on Cora.Source: §2 · p. 2, Figure 1 · p. 3
  • Grouping fragmented components or isolated nodes directly can mix different ground-truth communities or assign isolated nodes randomly.The paper notes that random grouping of isolated nodes renders community memberships random.Source: §2 · pp. 2–3
  • EdMot addresses fragmentation by leveraging motif-based structure while applying edge enhancement to the original network.Source: §2 · p. 3

3 THE PROPOSED METHOD

EdMot identifies and partitions the largest connected components of a motif-based hypergraph, then adds module-based edges to the original network. It partitions the rewired network to obtain communities while retaining lower-order connectivity; for triangle motifs, its stated overall complexity is O(m^1.5 + n log n).

3.1 Connected Component Identification

  • EdMot constructs a triangle-motif hypergraph, identifies its connected components and isolated nodes, then selects the top K components by node count for partitioning.Each selected component is partitioned into modules; the parameter K is analyzed later.Source: §3.1 · p. 3

3.2 Connected Component Partitioning

  • Louvain, which heuristically maximizes modularity [24] [25], is one example of a component partitioner; the resulting modules are aggregated, and other graph partitioning schemes may also be used.The modules only partially encode higher-order communities: different modules may belong to one ground-truth community, and nodes outside the selected components are not included.Source: §3.2 · pp. 3–4, §3.3 · p. 4

3.3 Network Rewiring via Edge Enhancement

  • EdMot adds clique edges within each module and retains the original edges, so the rewired network encodes both higher- and lower-order connectivity.The paper motivates stronger within-module connectivity by prioritizing motif-based connections, which it associates with social transitivity.Source: §3.4 · p. 4, §3.3 · p. 4

3.4 Method Summary and Computational Complexity

  • For triangle motifs, the stated overall complexity is O(m^1.5 + n log n), assuming O(1) graph-edge and matrix access; the rewired network is then partitioned into final communities.The complexity includes motif-instance discovery and graph partitioning.Source: §3.4 · p. 4

4 EXPERIMENTS

Experiments on eight real-world datasets compare EdMot variants with original and motif-based partitioning methods, using ground-truth labels where available and modularity otherwise. EdMot-Louvain performs strongly in comparisons, while the preferred K varies by dataset.

4.1 Datasets and Evaluation Measures

  • Eight undirected real-world datasets are evaluated; four have ground-truth labels and four use internal evaluation, including modularity.NMI and F-score require ground-truth labels; higher values indicate better performance for NMI, F-score, and modularity.Source: §4.1 · p. 5

4.2 Graph Partitioning Methods

  • Louvain, Spectral Clustering, Affinity Propagation, and NMF serve as graph partitioners for EdMot variants and corresponding motif-based variants.The original, motif-based, and EdMot versions of each partitioner are compared.Source: §4.2 · p. 6

4.3 Comparison Results

  • EdMot-Louvain achieves the best NMI, F-score, and modularity on polbooks, polblogs, and Cora; average NMI improves about 17% over Louvain and 14% over Motif-Louvain.On email-Eu-core, EdMot-Louvain performs worse than Motif-Louvain in NMI.Source: §4.3 · p. 6, Table 1 · p. 7
  • Overall, EdMot outperforms original and traditional higher-order partitioning methods when hypergraph fragmentation is present, and may improve some state-of-the-art methods without fragmentation.The comparison scores are averaged over 20 runs, with standard deviations reported.Source: §4.3 · p. 6

4.4 Parameter Analysis

  • For EdMot-Louvain, scores hardly change as K increases on polblogs and Cora; the best performance uses K=3 on as-22july06 and K=2 on email-Enron.Polbooks and email-Eu-core are omitted from the parameter discussion because their motif-based hypergraphs contain one connected component; K=1 is used for the other datasets.Source: §4.4 · pp. 6–7, Figure 3 · p. 6, Figure 4 · p. 6

5 RELATED WORK

Prior work ranges from lower-order clustering and partitioning methods to approaches that use network motifs. EdMot addresses fragmentation that can arise in motif-based hypergraphs while retaining higher-order connections.

5.1 Lower-Order Community Detection

  • Lower-order methods cluster using node and edge connectivity, with examples including Louvain, NMF, Affinity Propagation, Spectral Clustering, and stochastic blockmodels.The section also notes permanence-based and label-propagation methods.Source: §5.1 · p. 8

5.2 Motif-based Higher-Order Community Detection

  • Motif-based methods use small-subgraph connectivity, but fragmented motif hypergraphs can violate or underrepresent original lower-order structure; EdMot targets this issue.Prior approaches include motif modularity, motif-based sparsification, motif conductance, motif reweighting, and local higher-order partitioning.Source: §5.2 · p. 8

6 CONCLUSION

EdMot addresses fragmented motif-based hypergraphs by enhancing the original network’s connectivity before detecting communities. It uses modules from the largest hypergraph components to guide rewiring, then partitions the rewired network.

6 CONCLUSION

  • EdMot partitions the top K largest connected components of the motif-based hypergraph into modules, then constructs edges to derive a clique from each module.The components are selected by their number of contained nodes.Source: §6 · p. 8
  • The new edge set enhances the original network and produces a rewired network that leverages motif structure while addressing hypergraph fragmentation.The rewired network is then partitioned to obtain the higher-order community structure.Source: §6 · p. 8
  • The authors report extensive experiments to show the effectiveness of EdMot.Source: §6 · p. 8
Loading 1906.04560v1…