Feature-Based Network Construction: From Sampling to What-if Analysis

TL;DR

This paper introduces a gradient-based framework for reconstructing weighted networks from specified features, enabling exact sampling and what-if analysis, with applications demonstrated in social and financial networks.

Contribution

The paper presents the FBNC framework, a novel gradient-based method for feature-constrained network reconstruction and analysis, offering an alternative to exponential random graphs.

Findings

FBNC can sample networks satisfying given features exactly.

FBNC enables closest network adjustments for feature modifications.

Numerical experiments validate FBNC's effectiveness in social and financial networks.

Abstract

Networks are characterized by structural features, such as degree distribution, triangular closures, and assortativity. This paper addresses the problem of reconstructing instances of continuously (and non-negatively) weighted networks from given feature values. We introduce the gradient-based Feature-Based Network Construction (FBNC) framework. FBNC allows for sampling networks that satisfy prespecified features exactly (hard constraint sampling). Initializing the FBNC gradient descent with a random graph, FBNC can be used as an alternative to exponential random graphs in sampling graphs conditional on given feature values. We establish an implicit regularization approach to the original feature-fitting loss minimization problem so that FBNC achieves a parsimonious change in the underlying graph, where the term "implicit" stems from using appropriate norms in the very construction of the FBNC gradient descent. In constructing the implicit regularization, we distinguish between the case where weights of a link can be chosen from a bounded range, and, the more demanding case, where the weight matrix of the graph constitutes a Markov chain. We show that FBNC expands to "what-if analysis" of networks, that is, for a given initial network and a set of features satisfied by this network, FBNC finds the network closest to the initial network with some of the feature values adjusted or new features added. Numerical experiments in social network management and financial network regulation demonstrate the value of FBNC for graph (re)construction and what-if analysis.