Network clustering and community detection using modulus of families of loops

Shakeri, Heman; Poggi‐Corradini, Pietro; Albin, Nathan; Scoglio, Caterina

doi:10.1103/physreve.95.012316

Cited by 13 publications

(12 citation statements)

References 56 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These interactions correspond to induced subgraphs of networks that contain multiple vertices and edges and represent the information from different interactions among multiple vertices, and this kind of subgraph is also refered to as a motif [18]. The motif of a network is crucial to organization of complex networks [19], [20] and has a wide range of application scenarios in many fields, such as carbon exchange models in food chains, resource allocation in the Internet of Things [7], and analysis of small structures in social networks [21]. The use of motifs as atomic units in graph clustering is known as higher-order graph clustering.…”

Section: A Backgroundmentioning

confidence: 99%

“…If the unit is a node, then it is a graph cluster in the typical sense. Triangles are social and biological network motifs that play important roles [18], [21], [22]. In the current study, we use triangles as the main motifs, but to increase generality, we also use undirected quadrilaterals as motifs ( Figure 1).…”

Section: A Backgroundmentioning

confidence: 99%

“…If only one node is used as a seed, then the node that joins at the beginning might be a sparse node. Currently, the most commonly used method is to select a node and its neighbor node as seeds [11], [21], [34]. However, this method might introduce nodes that do not contribute.…”

Section: A Seed Phasementioning

confidence: 99%

See 2 more Smart Citations

Local Expansion and Optimization for Higher-Order Graph Clustering

Cai

et al. 2019

IEEE Internet Things J.

View full text Add to dashboard Cite

Graph clustering aims to identify clusters that feature tighter connections between internal nodes than external nodes. We noted that conventional clustering approaches based on a single vertex or edge cannot meet the requirements of clustering in a higher-order mixed structure formed by multiple nodes in a complex network. Considering the above limitation, we are aware of the fact that a clustering coefficient can measure the degree to which nodes in a graph tend to cluster, even if only a small area of the graph is given. In this study, we introduce a new cluster quality score, i.e., the local motif rate, which can effectively respond to the density of clusters in a higherorder graph. We also propose a motif-based local expansion and optimization algorithm (MLEO) to improve local higher-order graph clustering. This algorithm is a purely local algorithm and can be applied directly to higher-order graphs without conversion to a weighted graph, thus avoiding distortion of the transform. In addition, we propose a new seed-processing strategy in a higher-order graph. The experimental results show that our proposed strategy can achieve better performance than the existing approaches when using a quadrangle as the motif in the LFR network and the value of the mixing parameter µ exceeds 0.6.

show abstract

Section: A Backgroundmentioning

confidence: 99%

Section: A Backgroundmentioning

confidence: 99%

See 1 more Smart Citation

Local Expansion and Optimization for Higher-Order Graph Clustering

Cai

et al. 2019

IEEE Internet Things J.

View full text Add to dashboard Cite

show abstract

“…For the two-single-cell data Pollen&Treulin, the clustering results are related to the parameters of the KNN network, and the effect of k=10 is better than k=5. Now we consider the famous Zachary Karate Club network, which has become a common workbench for community search algorithms [39], [40]. The club network is divided into two parts by DCK, which are exactly the same as the original labels, as shown in Fig 4(a).…”

Section: B Real-world Networkmentioning

confidence: 99%

Community Detection and Visualization in Complex Network by the Density-Canopy-Kmeans Algorithm and MDS Embedding

Wang

Long

et al. 2019

IEEE Access

View full text Add to dashboard Cite

With the increasing availability of social networks and biological networks, detecting network community structure has become more and more important. However, most traditional methods for detecting community structure have limitations in dimension reduction or parameter optimization. In this paper, we propose a Density-Canopy-Kmeans clustering algorithm (DCK) to detect network community structure. Specifically, we define a novel distance metric, which integrates random distance and community structure coefficient based on the Jaccard distance. After applying the Multidimensional Scaling (MDS) dimension reduction, we cluster the nodes. KMEANS is combined with density clustering and canopy clustering to determine the optimal number of communities and the best initial seeds are determined to improve the accuracy and stability of the K-means algorithm. Compared with traditional community detection methods, our method has a higher classification accuracy and a better visualization effect. Thus, this method is effective for analyzing network communities. INDEX TERMS Network, community detection, the Density-Canopy-Kmeans clustering algorithm, MDS.

show abstract

“…-Loop modulus. Looking at families cycles in a graph gives information about clustering and community detection, see [22]. -Spanning tree modulus.…”

Section: Introductionmentioning

confidence: 99%

Blocking duality for p-modulus on networks and applications

Albin

Clemens

Fernando

et al. 2018

Annali di Matematica

Self Cite

View full text Add to dashboard Cite

This paper explores the implications of blocking duality-pioneered by Fulkerson et al.-in the context of p-modulus on networks. Fulkerson's blocking duality is an analogue on networks to the method of conjugate families of curves in the plane. The technique presented here leads to a general framework for studying families of objects on networks; each such family has a corresponding dual family whose p-modulus is essentially the reciprocal of the original family's.As an application, we give a modulus-based proof for the fact that effective resistance is a metric on graphs. This proof immediately generalizes to yield a family of graph metrics, depending on the parameter p, that continuously interpolates among the shortest-path metric, the effective resistance metric, and the mincut ultrametric. In a second application, we establish a connection between Fulkerson's blocking duality and the probabilistic interpretation of modulus. This connection, in turn, provides a straightforward proof of several monotonicity properties of modulus that generalize known monotonicity properties of effective resistance. Finally, we use this framework to expand on a result of Lovász in the context of randomly weighted graphs.2010 Mathematics Subject Classification. 90C27.

show abstract

Network clustering and community detection using modulus of families of loops

Cited by 13 publications

References 56 publications

Local Expansion and Optimization for Higher-Order Graph Clustering

Local Expansion and Optimization for Higher-Order Graph Clustering

Community Detection and Visualization in Complex Network by the Density-Canopy-Kmeans Algorithm and MDS Embedding

Blocking duality for p-modulus on networks and applications

Contact Info

Product

Resources

About