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Finding communities in weighted networks through synchronization
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View: Figures


Image of FIG. 1.
FIG. 1.

(Color online) A small synthetic network example with 9 labeled nodes. The numbers between two different nodes represent their coupling weights. The first four nodes are in the same community and highlighted in the same circles. The left five nodes are marked in another community.

Image of FIG. 2.
FIG. 2.

(Color online) Mutual information for partitions after applying the local weight ratio scheme on the LFR benchmark with undirected and weighted links. Each point is an average over 100 realizations.

Image of FIG. 3.
FIG. 3.

(Color online) (a) A weighted hierarchical network of 22 nodes with 5 communities. Each community is shaded with different colors. The edges are linked with different weights. The intra-community edges have larger weights than the inter-community edges. (b) Normalized dynamic affinity matrix St (T) in the weighted hierarchical network.

Image of FIG. 4.
FIG. 4.

(Color online) The dendrogram of community structure in the weighted hierarchical network found by our method. The dashed line corresponds to the optimal partition with maximal Qw  = 0.4947.

Image of FIG. 5.
FIG. 5.

(Color online) (a) The community structure of Zachary’s Karate Club network detected by the proposed method. (b) The dendrogram of the community structure found by our method.

Image of FIG. 6.
FIG. 6.

(Color online) The community structure of the network of interactions between major characters in the novel Les Misérables by Victor Hugo. The largest modularity achieved by using the locally weighted ratio scheme is Qw  = 0.5464 and corresponds to a 6-communities partition. Each community is shaded with a different color and a different shape.

Image of FIG. 7.
FIG. 7.

(Color online) The conference structure (a 9-communities partition) of the American football team network obtained by our method. Different communities are separated by dashed lines and each community is shaded with a different shape. Colors represent the real 12 conferences.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Finding communities in weighted networks through synchronization