Fig 1.
Zachary’s karate club structure obtained by FSh−Jk with nc = 3.
(a) Community 1, (b) Community 2, (c) Community 3.
Fig 2.
Configuration model example.
Fig 3.
Zachary’s karate club community structures.
Community structures obtained by (a) [15], (b) with parameters nc = 3, p = 2, (c)
with parameters nc = 3, p = 2.
Fig 4.
Zachary’s karate club disjoint community structures.
Community structures obtained by (a) with parameters nc = n, p = 1, (b)
with parameters nc = n, p = 1.
Fig 5.
Zachary’s karate club community structures.
Community structures obtained by (a) with parameters nc = 4, p = 2, (b)
with parameters nc = 4, p = 2.
Fig 6.
Community structures obtained by (a) with parameters nc = n, p = 1, (b)
with parameters nc = 3, p = 2, (c)
with parameters nc = 3, p = 2.
Fig 7.
Highland tribes community structures.
Community structures obtained by (a) with parameters nc = n, p = 1, (b)
with parameters nc = 3, p = 2.
Fig 8.
Windsurfers community structures.
Community structures obtained by (a) with parameters nc = n, p = 1, (b)
with parameters nc = 2, p = 2.
Table 1.
Computational results of the solution methods.
Fig 9.
American college football community structure.
Community structure obtained by LSE heuristic with weights and parameters nc = 7, p = 2.
Fig 10.
Jazz music community structure.
Community structure obtained by LSE heuristic with weights and parameters nc = 6, p = 2.
Fig 11.
C. metabolic community structure.
Community structure obtained by LSE heuristic with weights and parameters nc = 10, p = 2.
Table 2.
Computational results about networks with non-overlapping communities.
Fig 12.
Test results on non-overlapping communities, parameters N = 40, nc = 6.
(a) Average NMI for each solution method, (b) Average Omega for each solution method.
Fig 13.
Test results on non-overlapping communities, parameters N = 40, nc = 4.
(a) Average NMI for each solution method, (b) Average Omega for each solution method.
Fig 14.
Test results on non-overlapping communities, parameters N = 60, nc = 6.
(a) Average NMI for each solution method, (b) Average Omega for each solution method.
Table 3.
Computational results about networks with overlapping communities.
Fig 15.
Test results on overlapping communities, parameters p = 2, μo = 0.5, No = 1.
(a) Average NMI for each solution method, (b) Average Omega for each solution method.
Fig 16.
Test results on overlapping communities, parameters p = 2, μo = 0.5, No = 3.
(a) Average NMI for each solution method, (b) Average Omega for each solution method.
Fig 17.
Test results on overlapping communities, parameters p = 2, μo = 0.5, No = 5.
(a) Average NMI for each solution method, (b) Average Omega for each solution method.
Fig 18.
Test results on overlapping communities, parameters p = 2, μo = 0.7, No = 3.
(a) Average NMI for each solution method, (b) Average Omega for each solution method.
Fig 19.
Test results on overlapping communities, parameters p = 3, μo = 0.7, No = 3.
(a) Average NMI for each solution method, (b) Average Omega for each solution method.
Table 4.
Computational results about large-scale networks with overlapping communities.
Fig 20.
Test results on overlapping communities, parameters N = 500, nc = 25, p = 2, μo = 0.6, No = 20.
(a) Average NMI for each solution method, (b) Average Omega for each solution method.
Fig 21.
Test results on overlapping communities, parameters N = 500, nc = 25, p = 2, μo = 0.6, No = 50.
(a) Average NMI for each solution method, (b) Average Omega for each solution method.
Fig 22.
Test results on overlapping communities, parameters N = 500, nc = 25, p = 3, μo = 0.7, No = 20.
(a) Average NMI for each solution method, (b) Average Omega for each solution method.
Fig 23.
Test results on overlapping communities, parameters N = 1000, nc = 50, p = 2, μo = 0.6, No = 50.
(a) Average NMI for each solution method, (b) Average Omega for each solution method.
Table 5.
Computational results about large-scale networks with overlapping communities.