Change point detection in social networks—Critical review with experiments

Abstract

Change point detection in social networks is an important element in developing the understanding of dynamic systems. This complex and growing area of research has no clear guidelines on what methods to use or in which circumstances. This paper critically discusses several possible network metrics to be used for a change point detection problem and conducts an experimental, comparative analysis using the Enron and MIT networks. Bayesian change point detection analysis is conducted on different global graph metrics (Size, Density, Average Clustering Coefficient, Average Shortest Path) as well as metrics derived from the Hierarchical and Block models (Entropy, Edge Probability, No. of Communities, Hierarchy Level Membership). The results produced the posterior probability of a change point at weekly time intervals that were analysed against ground truth change points using precision and recall measures. Results suggest that computationally heavy generative models offer only slightly better results compared to some of the global graph metrics. The simplest metrics used in the experiments, i.e. nodes and links numbers, are the recommended choice for detecting overall structural changes.

The Settlement Structure Is Reflected in Personal Investments: Distance‐Dependent Network Modularity‐Based Measurement of Regional Attractiveness

“…This arrangement results in a transparent and easily interpretable network as people and companies are assigned to only one location. The resultant network describes how investments unite the locations; e.g., the adjacency matrix A [1] defines the number of links between the towns, and the degrees of the nodes represent the number of incoming and outgoing investments to the -th and from the -th town, respectively:…”

“…where [1] , represents the number of estimated investments proceeding from the -th to the -th town and…”

“…The critical element of the methodology is how the [1] , connection probabilities of the towns are calculated. The most widely applied null model is the random configuration model which calculates the edge probabilities assuming a random graph conditioned to preserve the degree sequence of the original network:…”

“…whose function is proportional to the weighted average of probability (1/ ) [1] , /( ) of a link existing at distance . When the distance dependence of the connection probability is handled by an explicit function, various modifications of the gravity law-based configuration model can be defined:…”

“…Mining valuable information from social networks is a hard problem due to its dynamic nature [1,2], complex structure [3,4], and multidimensionality [5]. This paper deals with the structural issues as it tries to evaluate regional attractiveness based on a set of goal-oriented null models identified to describe the geographical distributions of companyownership relations.…”