Disjoint and Non-Disjoint Community Detection with Control of Overlaps Between Communities

Finding Overlapping Communities Using Disjoint Community Detection Algorithms

Many algorithms have been designed to discover community structure in networks. Most of these detect disjoint communities, while a few can find communities that overlap. We propose a new, two-phase, method of detecting overlapping communities. In the first phase, a network is transformed to a new one by splitting vertices, using the idea of split betweenness; in the second phase, the transforme...

Leveraging disjoint communities for detecting overlapping community structure

Network communities represent mesoscopic structure for understanding the organization of real-world networks, where nodes often belong to multiple communities and form overlapping community structure in the network. Due to non-triviality in finding the exact boundary of such overlapping communities, this problem has become challenging, and therefore huge effort has been devoted to detect overla...

Combining Non-Disjoint Theories?

Disjoint Non-free Subgoups of Abelian Groups

Let G be an abelian group and let λ be the smallest rank of any group whose direct sum with a free group is isomorphic to G. If λ is uncountable, then G has λ pairwise disjoint, non-free subgroups. There is an example where λ is countably infinite and G does not have even two disjoint, non-free subgroups.

Non-minimal sums of disjoint products

We re…ne a conjecture of M. O. Locks and J. M. Wilson [Reliability Engineering and System Safety 46 (1994), 283-286] regarding disjoint forms of the Abraham Reliability problem. We also present other examples of reliability problems with the interesting property that their minimal disjoint forms do not arise from the familiar tautologyM1+:::+Mn M1+(M2 M1)+(M3 M2 M1)+:::+(Mn Mn 1 ::: M1):