A Set-Theoretic Approach to Modeling Network Structure

Abstract

Three computer algorithms are presented. One reduces a network N to its interior, I. Another counts all the triangles in a network, and the last randomly generates networks similar to N given just its interior I. However, these algorithms are not the usual numeric programs that manipulate a matrix representation of the network; they are set-based. Union and meet are essential binary operators; contained_in is the basic relational comparator. The interior I is shown to have desirable formal properties and to provide an effective way of revealing “communities” in social networks. A series of networks randomly generated from I is compared with the original network, N.

Keywords

• interior
• reduction
• weak links
• closure
• communities