A unit two variable per inequality (UTVPI) constraint is of the form a.x+b.y ≤ d where x and y are integer variables, the coefficients a, b ∈ {−1, 0, 1} and the bound d is an integer constant. This paper presents an efficient decision procedure for UTVPI constraints. Given m such constraints over n variables, the procedure checks the satisfiability of the constraints in O(n.m) time and O(n+m) s...

The widely-used notion of triadic closure has been conceptualized and measured in a variety of ways, most famously the clustering coefficient. This paper proposes a measure of triadic closure in affiliation networks designed to control for the influence of bicliques. In order to avoid arbitrariness, the paper introduces a triadic framework for affiliation networks, within which a range of possi...

When users interact with one another on social media sites, the volume and frequency of their communication can shift over time, as their interaction strengthens or weakens. We study the interplay of several competing factors in the maintainance of such links, developing a methodology that can begin to separate out the effects of several distinct social forces. In particular, if two users devel...

This paper uses a social network approach to examine gender clustering in a complete network of teenagers and their friends. It demonstrates the advantages of using increasingly sophisticated social network techniques, including clustering coefficients and their visualization, and social selection models within the ERGM framework, to visualize and explain the process of clustering which takes p...

In social networks the Strong Triadic Closure is an assignment of the edges with strong or weak labels such that any two vertices that have a common neighbor with a strong edge are adjacent. The problem of maximizing the number of strong edges that satisfy the strong triadic closure was recently shown to be NP-complete for general graphs. Here we initiate the study of graph classes for which th...

Mechanisms such as triadic closure and preferential attachment drive the evolution of social networks. Many models use these mechanisms to predict future links, and they generate realistic networks with scale-free degree distributions. These social networks also have community structure, or sets of vertices which are more connected to each other than the rest of the network. To study the evolut...

A long-standing debate has taken place in the organizational sociology and social network literatures about the relative advantages of network closure versus structural holes in the generation of social capital. There is recent evidence that these advantages differ across cultures and between East Asia and the West in particular, but existing network models are unable to explain why or address ...