Entropic graph embedding via multivariate degree distributions

Although there are many existing alternative methods for using structural characterizations of undirected graphs for embedding, clustering and classification problems, there is relatively little literature aimed at dealing with such problems for directed graphs. In this paper we present a novel method for characterizing graph structure that can be used to embed directed graphs into a feature space. The method commences from a characterization based on the distribution of the von Neumann entropy of a directed graph with the in and out-degree configurations associated with directed edges. We start from a recently developed expression for the von Neumann entropy of a directed graph, which depends on vertex in-degree and out-degree statistics, and thus obtain a multivariate edge-based distribution of entropy. We show how this distribution can be encoded as a multi-dimensional histogram, which captures the structure of a directed graph and reflects its complexity. By performing principal components analysis on a sample of histograms, we embed populations of directed graphs into a low dimensional space. Finally, we undertake experiments on both artificial and real-world data to demonstrate that our directed graph embedding method is effective in distinguishing different types of directed graphs

Towards an approximate graph entropy measure for identifying incidents in network event data

A key objective of monitoring networks is to identify potential service threatening outages from events within the network before service is interrupted. Identifying causal events, Root Cause Analysis (RCA), is an active area of research, but current approaches are vulnerable to scaling issues with high event rates. Elimination of noisy events that are not causal is key to ensuring the scalability of RCA. In this paper, we introduce vertex-level measures inspired by Graph Entropy and propose their suitability as a categorization metric to identify nodes that are a priori of more interest as a source of events. We consider a class of measures based on Structural, Chromatic and Von Neumann Entropy. These measures require NP-Hard calculations over the whole graph, an approach which obviously does not scale for large dynamic graphs that characterise modern networks. In this work we identify and justify a local measure of vertex graph entropy, which behaves in a similar fashion to global measures of entropy when summed across the whole graph. We show that such measures are correlated with nodes that generate incidents across a network from a real data set

Thermodynamic Analysis of Time Evolving Networks

The problem of how to represent networks, and from this representation, derive succinct characterizations of network structure and in particular how this structure evolves with time, is of central importance in complex network analysis. This paper tackles the problem by proposing a thermodynamic framework to represent the structure of time-varying complex networks. More importantly, such a framework provides a powerful tool for better understanding the network time evolution. Specifically, the method uses a recently-developed approximation of the network von Neumann entropy and interprets it as the thermodynamic entropy for networks. With an appropriately-defined internal energy in hand, the temperature between networks at consecutive time points can be readily derived, which is computed as the ratio of change of entropy and change in energy. It is critical to emphasize that one of the main advantages of the proposed method is that all these thermodynamic variables can be computed in terms of simple network statistics, such as network size and degree statistics. To demonstrate the usefulness of the thermodynamic framework, the paper uses real-world network data, which are extracted from time-evolving complex systems in the financial and biological domains. The experimental results successfully illustrate that critical events, including abrupt changes and distinct periods in the evolution of complex networks, can be effectively characterized