Exploring the structure and function of temporal networks with dynamic graphlets

Abstract

Motivation: With increasing availability of temporal real-world networks, how to efficiently study these data? One can model a temporal network as a single aggregate static network, or as a series of time-specific snapshots, each being an aggregate static network over the corresponding time window. Then, one can use established methods for static analysis on the resulting aggregate network(s), but losing in the process valuable temporal information either completely, or at the interface between different snapshots, respectively. Here, we develop a novel approach for studying a temporal network more explicitly, by capturing inter-snapshot relationships.Results: We base our methodology on well-established graphlets (subgraphs), which have been proven in numerous contexts in static network research. We develop new theory to allow for graphlet-based analyses of temporal networks. Our new notion of dynamic graphlets is different from existing dynamic network approaches that are based on temporal motifs (statistically significant subgraphs). The latter have limitations: their results depend on the choice of a null network model that is required to evaluate the significance of a subgraph, and choosing a good null model is non-trivial. Our dynamic graphlets overcome the limitations of the temporal motifs. Also, when we aim to characterize the structure and function of an entire temporal network or of individual nodes, our dynamic graphlets outperform the static graphlets. Clearly, accounting for temporal information helps. We apply dynamic graphlets to temporal age-specific molecular network data to deepen our limited knowledge about human aging.Availability and implementation: http://www.nd.edu/∼cone/DG.Contact: tmilenko@nd.eduSupplementary information: Supplementary data are available at Bioinformatics online.

Supervised prediction of aging-related genes from a context-specific protein interaction subnetwork

“…Finally, we examine our hypothesis 3, which was already confirmed in an unsupervised analysis of the same agingspecific subnetworks [24]. To validate it in our supervised analysis, it would suffice for the best feature on the dynamic subnetwork to be superior to the best feature on the static subnetwork.…”

“…For each aging-related and non-aging-related gene, we use eight features that, while not novel to our study, have not yet been used in this study's task of supervised prediction of aging-related genes. Among them, seven are dynamic, i.e., extracted from the dynamic aging-specific subnetwork: dynamic graphlet degree vector (DGDV) [24], graphlet orbit transitions (GoT) [25], graphlet degree centrality (GDC) [26], eccentricity (ECC), k-core (KC), degree centrality (DegC), and centrality mean and variation (CentraMV) [4]. The remaining feature is static, i.e., extracted from the static aging-specific subnetwork and the entire (also static) PPI network: static graphlet degree vector (SGDV) [27].…”

“…Clearly, the mutation driver genes are a subset of the all driver genes. • DGDV of a node [24] counts how many times the node participates in (touches) each dynamic graphlet on up to n nodes and e events (temporal edges), i.e., in each of the given graphlet's topologically unique node positions called automorphism orbits. Dynamic graphlets are an extension of static graphlets, i.e., up to n-node subgraphs of a static network, to the dynamic setting, with temporal information added onto edges of static graphlets; this information indicates the temporal order in which events occur in a dynamic network.…”

Identification of co-evolving temporal networks

“…To address this oversight, we define a biological network using a model that accounts for the evolution of the underlying network at consecutive time points. We refer to this model as a temporal network (Hulovatyy et al, 2015). We view this model as containing a single snapshot of the network at each time point in a sequence of time points and thus, as a time series network.…”

Clone temporal centrality measures for incomplete sequences of graph snapshots

“…For this purpose, a dynamic network is often represented as a dynamic graph consisting of a vertex set V and a temporal edge set E . While some authors [5, 6] define a temporal edge as event between two vertices a and b starting at a particular time point with specific edge duration, others [7–9] define a dynamic network as a sequence of static graphs, so called snapshots, consisting of temporal edge sets E t . The temporal order of the edge set describes the direction of the dynamics.…”