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Localization of hubs in complex networks with overlapping modular structure

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HAL Id: hal-03059191

https://hal.archives-ouvertes.fr/hal-03059191

Submitted on 13 Dec 2020

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Localization of hubs in complex networks with overlapping modular structure

Zakariya Ghalmane, Chantal Cherifi, Hocine Cherifi, Mohammed El Hassouni

To cite this version:

Zakariya Ghalmane, Chantal Cherifi, Hocine Cherifi, Mohammed El Hassouni. Localization of hubs in complex networks with overlapping modular structure. NetSci International School and Conference on Network Science, Sep 2020, Rome (Online), Italy. pp.1. �hal-03059191�

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Localization of hubs in complex networks with overlapping modular structure

Zakariya Ghalmane Mohammed El Hassouni Chantal Cherifi Hocine Cherifi

University Mohammed V MOROCCO University of Lyon 2 FRANCE University of Burgundy FRANCE

Overlapping nodes

C

1

C

3

C

2

C

4

? Hubs

Problematic

Evaluation measures

Community detection

Ego-network of overlapping nodes

&

List of Hubs

Proportion of hubs Rank-biased overlap

Correlation

Degree distribution

Methodology

Empirical Networks

Results

Proportion of hubs Rank-biased overlap

Correlation

Degree distribution

University Mohammed V MOROCCO University of Burgundy FRANCE

Small Network Medium Network Large Network

Ego-Facebook network

Karate network Condense Matter network

Social network

N 34 E 78

Non Assortative Relatively high

density

Social network

N 4039 E 88234

Assortative Small density

Collaboration network

N 23133 E 93497

Assortative Very small

density

Overlapping nodes

Hubs

p = 77.6 %

P. overlapping nodes: 14.7 %

P. overlapping nodes (%)

Proportion of hubs (%)

ego-Facebook 3.1 59.25

ca-CondMat 2.1 79.57

Network

Network RBO

p=0.5 p=0.8 p=0.98 Karate club 0.998 0.952 0.844 Ego-facebook 0.998 0.952 0.844 ca-CondMat 1 0.999 0.999

Network Pearson Correlation

Spearman Correlation Karate club 0.991 0.98

ego-Facebook 0.985 0.98 ca-CondMat 0.989 0.99

Neighbors of the overlapping nodes

Hubs

Power law distribution

Ghalmane, Z., Cherifi, C., Cherifi, H., & El Hassouni, M. (2020). Exploring Hubs and Overlapping Nodes Interactions in Modular Complex Networks. IEEE

Access, 8, 79650-79683.

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