Compute highly connected subgraphs for an undirected graph
Compute highly connected subgraphs for an undirected graph
highlyConnSG(g, sat=3, ldv=c(3,2,1))
g |
an instance of the |
sat |
singleton adoption threshold, positive integer |
ldv |
heuristics to remove lower degree vertice, a decreasing sequence of positive integer |
A graph G with n vertices is highly connected if its connectivity k(G) > n/2. The HCS algorithm partitions a given graph into a set of highly connected subgraphs, by using minimum-cut algorithm recursively. To improve performance, the approach is refined by adopting singletons, removing low degree vertices and merging clusters.
On singleton adoption: after each round of partition, some highly connected subgraphs could be singletons (i.e., a subgraph contains only one node). To reduce the number of singletons, therefore reduce number of clusters, we try to get "normal" subgraphs to "adopt" them. If a singleton, s, has n neighbours in a highly connected subgraph c, and n > sat, we add s to c. To adapt to the modified subgraphs, this adoption process is repeated until no further such adoption.
On lower degree vertices: when the graph has low degree vertices, minimum-cut algorithm will just repeatedly separate these vertices from the rest. To reduce such expensive and non-informative computation, we "remove" these low degree vertices first before applying minimum-cut algorithm. Given ldv = (d1, d2, ..., dp), (d[i] > d[i+1] > 0), we repeat the following (i from 1 to p): remove all the highly-connected-subgraph found so far; remove vertices with degrees < di; find highly-connected-subgraphs; perform singleton adoptions.
The Boost implementation does not support self-loops, therefore we
signal an error and suggest that users remove self-loops using the
function removeSelfLoops function. This change does affect
degree, but the original article makes no specific reference to self-loops.
A list of clusters, each is given as vertices in the graph.
Li Long <li.long@isb-sib.ch>
A Clustering Algorithm based on Graph Connectivity by E. Hartuv, R. Shamir, 1999.
con <- file(system.file("XML/hcs.gxl",package="RBGL"))
coex <- fromGXL(con)
close(con)
highlyConnSG(coex)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.