When is a Network a Network? Multi-Order Graphical Model Selection in Pathways and Temporal Networks

TL;DR

This paper introduces a multi-layer graphical modeling framework for sequential network data, capturing multi-scale temporal correlations and providing a principled method for network abstraction validation.

Contribution

It proposes a novel multi-order graphical model selection technique that outperforms existing methods and clarifies when network abstractions are justified for sequential data.

Findings

The model effectively captures both topological and temporal features of pathways.

It outperforms previous Markov order detection techniques.

Application to real-world data demonstrates its practical utility.

Abstract

We introduce a framework for the modeling of sequential data capturing pathways of varying lengths observed in a network. Such data are important, e.g., when studying click streams in information networks, travel patterns in transportation systems, information cascades in social networks, biological pathways or time-stamped social interactions. While it is common to apply graph analytics and network analysis to such data, recent works have shown that temporal correlations can invalidate the results of such methods. This raises a fundamental question: when is a network abstraction of sequential data justified? Addressing this open question, we propose a framework which combines Markov chains of multiple, higher orders into a multi-layer graphical model that captures temporal correlations in pathways at multiple length scales simultaneously. We develop a model selection technique to infer the optimal number of layers of such a model and show that it outperforms previously used Markov order detection techniques. An application to eight real-world data sets on pathways and temporal networks shows that it allows to infer graphical models which capture both topological and temporal characteristics of such data. Our work highlights fallacies of network abstractions and provides a principled answer to the open question when they are justified. Generalizing network representations to multi-order graphical models, it opens perspectives for new data mining and knowledge discovery algorithms.