Exploring the structure and function of temporal networks with dynamic graphlets

With the growing amount of available temporal real-world network data, an important question is how to efficiently study these data. One can simply model a temporal network as either a single aggregate static network, or as a series of time-specific snapshots, each of which is an aggregate static network over the corresponding time window. The advantage of modeling the temporal data in these two ways is that one can use existing well established methods for static network analysis to study the resulting aggregate network(s). Here, we develop a novel approach for studying temporal network data more explicitly. We base our methodology on the well established notion of graphlets (subgraphs), which have been successfully used in numerous contexts in static network research. Here, we take the notion of static graphlets to the next level and develop new theory needed to allow for graphlet-based analysis of temporal networks. Our new notion of dynamic graphlets is quite different than existing approaches for dynamic network analysis that are based on temporal motifs (statistically significant subgraphs). Namely, these approaches suffer from many limitations. For example, they can only deal with subgraph structures of limited complexity. Also, their major drawback is that their results heavily depend on the choice of a null network model that is required to evaluate the significance of a subgraph. However, choosing an appropriate null network model is a non-trivial task. Our dynamic graphlet approach overcomes the limitations of the existing temporal motif-based approaches. At the same time, when we thoroughly evaluate the ability of our new approach to characterize the structure and function of an entire temporal network or of individual nodes, we find that the dynamic graphlet approach outperforms the static graphlet approach, which indicates that accounting for temporal information helps

Network comparison using directed graphlets

With recent advances in high-throughput cell biology the amount of cellular biological data has grown drastically. Such data is often modeled as graphs (also called networks) and studying them can lead to new insights into molecule-level organization. A possible way to understand their structure is by analysing the smaller components that constitute them, namely network motifs and graphlets. Graphlets are particularly well suited to compare networks and to assess their level of similarity but are almost always used as small undirected graphs of up to five nodes, thus limiting their applicability in directed networks. However, a large set of interesting biological networks such as metabolic, cell signaling or transcriptional regulatory networks are intrinsically directional, and using metrics that ignore edge direction may gravely hinder information extraction. The applicability of graphlets is extended to directed networks by considering the edge direction of the graphlets. We tested our approach on a set of directed biological networks and verified that they were correctly grouped by type using directed graphlets. However, enumerating all graphlets in a large network is a computationally demanding task. Our implementation addresses this concern by using a state-of-the-art data structure, the g-trie, which is able to greatly reduce the necessary computation. We compared our tool, gtrieScanner, to other state-of-the art methods and verified that it is the fastest general tool for graphlet counting.Comment: 9 page

Temporal Network Comparison using Graphlet-orbit Transitions

Networks are widely used to model real-world systems and uncover their topological features. Network properties such as the degree distribution and shortest path length have been computed in numerous real-world networks, and most of them have been shown to be both scale-free and small-world networks. Graphlets and network motifs are subgraph patterns that capture richer structural information than aforementioned global network properties, and these local features are often used for network comparison. However, past work on graphlets and network motifs is almost exclusively applicable only for static networks. Many systems are better represented as temporal networks which depict not only how a system was at a given stage but also how they evolved. Time-dependent information is crucial in temporal networks and, by disregarding that data, static methods can not achieve the best possible results. This paper introduces an extension of graphlets for temporal networks. Our proposed method enumerates all 4-node graphlet-orbits in each network-snapshot, building the corresponding orbit-transition matrix in the process. Our hypothesis is that networks representing similar systems have characteristic orbit transitions which better identify them than simple static patterns, and this is assessed on a set of real temporal networks split into categories. In order to perform temporal network comparison we put forward an orbit-transition-agreement metric (OTA). OTA correctly groups a set of temporal networks that both static network motifs and graphlets fail to do so adequately. Furthermore, our method produces interpretable results which we use to uncover characteristic orbit transitions, and that can be regarded as a network-fingerprint

Improving supervised prediction of aging-related genes via dynamic network analysis

This study focuses on supervised prediction of aging-related genes from -omics data. Unlike gene expression methods that capture aging-specific information but study genes in isolation, or protein-protein interaction (PPI) network methods that account for PPIs but the PPIs are context-unspecific, we recently integrated the two data types into an aging-specific PPI subnetwork, which yielded more accurate aging-related gene predictions. However, a dynamic aging-specific subnetwork did improve prediction performance compared to a static aging-specific subnetwork, despite the aging process being dynamic. So, here, we propose computational advances towards improving prediction accuracy from a dynamic aging-specific subnetwork. We develop a supervised learning model that when applied to a dynamic subnetwork yields extremely high prediction performance, with F-score of 91.4%, while the best model on any static subnetwork yields F-score of "only" 74.3%. Hence, our predictive model could guide with high confidence the discovery of novel aging-related gene candidates for future wet lab validation

A sampling framework for counting temporal motifs

Pattern counting in graphs is fundamental to network science tasks, and there are many scalable methods for approximating counts of small patterns, often called motifs, in large graphs. However, modern graph datasets now contain richer structure, and incorporating temporal information in particular has become a critical part of network analysis. Temporal motifs, which are generalizations of small subgraph patterns that incorporate temporal ordering on edges, are an emerging part of the network analysis toolbox. However, there are no algorithms for fast estimation of temporal motifs counts; moreover, we show that even counting simple temporal star motifs is NP-complete. Thus, there is a need for fast and approximate algorithms. Here, we present the first frequency estimation algorithms for counting temporal motifs. More specifically, we develop a sampling framework that sits as a layer on top of existing exact counting algorithms and enables fast and accurate memory-efficient estimates of temporal motif counts. Our results show that we can achieve one to two orders of magnitude speedups with minimal and controllable loss in accuracy on a number of datasets.Comment: 9 pages, 4 figure

Graphlets versus node2vec and struc2vec in the task of network alignment

Network embedding aims to represent each node in a network as a low-dimensional feature vector that summarizes the given node's (extended) network neighborhood. The nodes' feature vectors can then be used in various downstream machine learning tasks. Recently, many embedding methods that automatically learn the features of nodes have emerged, such as node2vec and struc2vec, which have been used in tasks such as node classification, link prediction, and node clustering, mainly in the social network domain. There are also other embedding methods that explicitly look at the connections between nodes, i.e., the nodes' network neighborhoods, such as graphlets. Graphlets have been used in many tasks such as network comparison, link prediction, and network clustering, mainly in the computational biology domain. Even though the two types of embedding methods (node2vec/struct2vec versus graphlets) have a similar goal -- to represent nodes as features vectors, no comparisons have been made between them, possibly because they have originated in the different domains. Therefore, in this study, we compare graphlets to node2vec and struc2vec, and we do so in the task of network alignment. In evaluations on synthetic and real-world biological networks, we find that graphlets are both more accurate and faster than node2vec and struc2vec

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

Background. Human aging is linked to many prevalent diseases. The aging process is highly influenced by genetic factors. Hence, it is important to identify human aging-related genes. We focus on supervised prediction of such genes. Gene expression-based methods for this purpose study genes in isolation from each other. While protein-protein interaction (PPI) network-based methods for this purpose account for interactions between genes' protein products, current PPI network data are context-unspecific, spanning different biological conditions. Instead, here, we focus on an aging-specific subnetwork of the entire PPI network, obtained by integrating aging-specific gene expression data and PPI network data. The potential of such data integration has been recognized but mostly in the context of cancer. So, we are the first to propose a supervised learning framework for predicting aging-related genes from an aging-specific PPI subnetwork. Results. In a systematic and comprehensive evaluation, we find that in many of the evaluation tests: (i) using an aging-specific subnetwork indeed yields more accurate aging-related gene predictions than using the entire network, and (ii) predictive methods from our framework that have not previously been used for supervised prediction of aging-related genes outperform existing prominent methods for the same purpose. Conclusion. These results justify the need for our framework.Comment: This is a Journal extension of "10.1109/BIBM47256.2019.8983063". So we use the same title as our conference pape

On the Enumeration of Maximal (Δ,γ)(\Delta, \gamma)-Cliques of a Temporal Network

A temporal network is a mathematical way of precisely representing a time varying relationship among a group of agents. In this paper, we introduce the notion of $(\Delta, \gamma)$-Cliques of a temporal network, where every pair of vertices present in the clique communicates atleast $\gamma$ times in each $\Delta$ period within a given time duration. We present an algorithm for enumerating all such maximal cliques present in the network. We also implement the proposed algorithm with three human contact network data sets. Based on the obtained results, we analyze the data set on multiple values of $\Delta$ and $\gamma$, which helps in finding out contact groups with different frequencies.Comment: 9 pages. Both the authors have done equal contributions in this wor

Network-based protein structural classification

Experimental determination of protein function is resource-consuming. As an alternative, computational prediction of protein function has received attention. In this context, protein structural classification (PSC) can help, by allowing for determining structural classes of currently unclassified proteins based on their features, and then relying on the fact that proteins with similar structures have similar functions. Existing PSC approaches rely on sequence-based or direct 3-dimensional (3D) structure-based protein features. In contrast, we first model 3D structures of proteins as protein structure networks (PSNs). Then, we use network-based features for PSC. We propose the use of graphlets, state-of-the-art features in many research areas of network science, in the task of PSC. Moreover, because graphlets can deal only with unweighted PSNs, and because accounting for edge weights when constructing PSNs could improve PSC accuracy, we also propose a deep learning framework that automatically learns network features from weighted PSNs. When evaluated on a large set of ~9,400 CATH and ~12,800 SCOP protein domains (spanning 36 PSN sets), our proposed approaches are superior to existing PSC approaches in terms of accuracy, with comparable running time

ITeM: Independent Temporal Motifs to Summarize and Compare Temporal Networks

Networks are a fundamental and flexible way of representing various complex systems. Many domains such as communication, citation, procurement, biology, social media, and transportation can be modeled as a set of entities and their relationships. Temporal networks are a specialization of general networks where the temporal evolution of the system is as important to understand as the structure of the entities and relationships. We present the Independent Temporal Motif (ITeM) to characterize temporal graphs from different domains. The ITeMs are edge-disjoint temporal motifs that can be used to model the structure and the evolution of the graph. For a given temporal graph, we produce a feature vector of ITeM frequencies and apply this distribution to the task of measuring the similarity of temporal graphs. We show that ITeM has higher accuracy than other motif frequency-based approaches. We define various metrics based on ITeM that reveal salient properties of a temporal network. We also present importance sampling as a method for efficiently estimating the ITeM counts. We evaluate our approach on both synthetic and real temporal networks