What is the drawback of to Minimum-Cut method? If community sizes are unconstrained. a division that puts just one vertex in one group and the rest in the other will often be limits optimal the community structure problem differs crucially from graph partitioning in that the sizes of the communities are not normally known in advance 6
limits the community structure problem differs crucially from graph partitioning in that the sizes of the communities are not normally known in advance. To If community sizes are unconstrained, a division that puts just one vertex in one group and the rest in the other will often be optimal. What is the drawback of Minimum-Cut Method?
2)GN Algorithm The Girvan-Newman (Gn)algorithm identifies heavy? edges in a network that lie between communities and then removes them, leaving only the communities This is a betweenness-based clustering method Identification is performed by employing the edge betweenness, yielding results of reasonable quality Drawbacks: High computational complexity M. Girvan and M. E J. Newman, PNAS, 99(12): 7821-7826, 2002
2) GN Algorithm The Girvan-Newman (GN) algorithm identifies “heavy” edges in a network that lie between communities and then removes them, leaving only the communities This is a betweenness-based clustering method: Identification is performed by employing the edgebetweenness, yielding results of reasonable quality Drawbacks: High computational complexity M. Girvan and M. E. J. Newman, PNAS, 99(12): 7821-7826, 2002
GN Algorithm 1 Calculate all the edge-betweenness in the network 2 Remove the edge with the highest betweenness 3 Re-calculate all the edge-betweennesses for the resulting(smaller) network 4 Repeat the above until no edge is left 3 5 5 Question: How to divide the network into two communities with the gn algorithm
GN Algorithm 1 Calculate all the edge-betweenness in the network 2 3 4 Remove the edge with the highest betweenness Re-calculate all the edge-betweennesses for the resulting (smaller) network Repeat the above, until no edge is left Question： How to divide the network into two communities with the GN algorithm？
vI Remove(5)v2-v4, v3-V5 1 Remove(2)v4-v6, v5-v6 v4 Remove(1)v1-v2, v2-V3, v3-VI Net Remove v2-v4 v3-v5 V1,v2,v3 v4, v5. v6 2 communities Remove v1-v2, v2-v3, v3-v1 Remove v4-16, v5-v6 v1 V2 V 3 v4 15 v6)6 communities
Remove (5) v2-v4, v3-v5 Remove (2) v4-v6, v5-v6 Remove (1) v1-v2, v2-v3, v3-v1 Net v1 v1,v2,v3 v4,v5,v6 v2 v3 v4 v5 v6 2 communities 6 communities Remove v2-v4, v3-v5 Remove v1-v2, v2-v3, v3-v1 Remove v4-v6, v5-v6
3)Modularity Maximization ce one of the most widel Modularity Maximization Method used methods for dividing Detects communities by networks into parts searching over possible divisions of a network for those that have particularly highest modularity Modularity Fast Unfolding Community Detection Algorithm a popular modularity maximization a benefit function that measures approach which iteratively y the quality of a particular division optimizes local communities until of network into communications global modularity can not be further improved
20 Modularity Maximization Method Fast Unfolding Community Detection Algorithm a benefit function that measures the quality of a particular division of network into communications Modularity 3) Modularity Maximization One of the most widely used methods for dividing networks into parts. Detects communities by searching over possible divisions of a network for those that have particularly highest modularity A popular modularity maximization approach, which iteratively optimizes local communities until global modularity can not be further improved