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

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.Comment: 10 pages, 4 figures, 1 table, companion python package pathpy available on gitHu

Analysis of Neighbourhoods in Multi-layered Dynamic Social Networks

Social networks existing among employees, customers or users of various IT systems have become one of the research areas of growing importance. A social network consists of nodes - social entities and edges linking pairs of nodes. In regular, one-layered social networks, two nodes - i.e. people are connected with a single edge whereas in the multi-layered social networks, there may be many links of different types for a pair of nodes. Nowadays data about people and their interactions, which exists in all social media, provides information about many different types of relationships within one network. Analysing this data one can obtain knowledge not only about the structure and characteristics of the network but also gain understanding about semantic of human relations. Are they direct or not? Do people tend to sustain single or multiple relations with a given person? What types of communication is the most important for them? Answers to these and more questions enable us to draw conclusions about semantic of human interactions. Unfortunately, most of the methods used for social network analysis (SNA) may be applied only to one-layered social networks. Thus, some new structural measures for multi-layered social networks are proposed in the paper, in particular: cross-layer clustering coefficient, cross-layer degree centrality and various versions of multi-layered degree centralities. Authors also investigated the dynamics of multi-layered neighbourhood for five different layers within the social network. The evaluation of the presented concepts on the real-world dataset is presented. The measures proposed in the paper may directly be used to various methods for collective classification, in which nodes are assigned to labels according to their structural input features.Comment: 16 pages, International Journal of Computational Intelligence System

Node Embedding over Temporal Graphs

In this work, we present a method for node embedding in temporal graphs. We propose an algorithm that learns the evolution of a temporal graph's nodes and edges over time and incorporates this dynamics in a temporal node embedding framework for different graph prediction tasks. We present a joint loss function that creates a temporal embedding of a node by learning to combine its historical temporal embeddings, such that it optimizes per given task (e.g., link prediction). The algorithm is initialized using static node embeddings, which are then aligned over the representations of a node at different time points, and eventually adapted for the given task in a joint optimization. We evaluate the effectiveness of our approach over a variety of temporal graphs for the two fundamental tasks of temporal link prediction and multi-label node classification, comparing to competitive baselines and algorithmic alternatives. Our algorithm shows performance improvements across many of the datasets and baselines and is found particularly effective for graphs that are less cohesive, with a lower clustering coefficient