Inferring Network Topology Research Articles

A comparative analysis of knowledge acquisition performance in complex networks

Discovery processes have been an important topic in the network science field. The exploration of nodes can be understood as the knowledge acquisition process taking place in the network, where nodes represent concepts and edges are the semantical relationships between concepts. While some studies have analyzed the performance of the knowledge acquisition process in particular network topologies, here we performed a systematic performance analysis in well-known dynamics and topologies. Several interesting results have been found. Overall, all learning curves displayed the same learning shape, with different speed rates. We also found ambiguities in the feature space describing the learning curves, meaning that the same knowledge acquisition curve can be generated in different combinations of network topology and dynamics. A surprising example of such patterns are the learning curves obtained from random and Waxman networks: despite the very distinct characteristics in terms of global structure, several curves from different models turned out to be similar. All in all, our results suggest that different learning strategies can lead to the same learning performance. From the network reconstruction point of view, however, this means that learning curves of observed sequences should be combined with other sequence features if one aims at inferring network topology from observed sequences.

Network Topology Inference Based on Subset Structure Fusion

Network topology measurement is an important component in network research. Network tomography is able to accurately infer network topology by using end-to-end measurement without cooperation of internal routers. Unfortunately, traditional network tomography methods can not accurately estimate topology in the non-stationary network due to the variability of traffic distribution. In this paper, we present a novel network topology inference method based on subset structure fusion for accurate topology inference in the non-stationary network. First, we propose an end-to-end measurement method named three-packet to accurately probe the three-leaf-nodes subset structures of the network without the assumption that the packet delay or loss follows a stable distribution. Second, we propose a metric for the shared path length based on the structural characteristics of the subset structures to fuse these subset structures into a correct complete topology. The analytical and simulation results show that our method is more applicable for topology inference in the non-stationary network compared with the existing methods.

Network topology inference using information cascades with limited statistical knowledge

AbstractWe study the problem of inferring network topology from information cascades, in which the amount of time taken for information to diffuse across an edge in the network follows an unknown distribution. Unlike previous studies, which assume knowledge of these distributions, we only require that diffusion along different edges in the network be independent together with limited moment information (e.g. the means). We introduce the concept of a separating vertex set for a graph, which is a set of vertices in which for any two given distinct vertices of the graph there exists a vertex whose distance to them is different. We show that a necessary condition for reconstructing a tree perfectly using distance information between pairs of vertices is given by the size of an observed separating vertex set. We then propose an algorithm to recover the tree structure using infection times whose differences have means corresponding to the distance between two vertices. To improve the accuracy of our algorithm, we propose the concept of redundant vertices, which allows us to perform averaging to better estimate the distance between two vertices. Though the theory is developed mainly for tree networks, we demonstrate how the algorithm can be extended heuristically to general graphs. Simulations using synthetic and real networks and experiments using real-world data suggest that our proposed algorithm performs better than some current state-of-the-art network reconstruction methods.

Inferring network topology via the propagation process

Inferring the network topology from the dynamics is a fundamental problem, with wide applications in geology, biology, and even counter-terrorism. Based on the propagation process, we present a simple method to uncover the network topology. A numerical simulation on artificial networks shows that our method enjoys a high accuracy in inferring the network topology. We find that the infection rate in the propagation process significantly influences the accuracy, and that each network corresponds to an optimal infection rate. Moreover, the method generally works better in large networks. These finding are confirmed in both real social and nonsocial networks. Finally, the method is extended to directed networks, and a similarity measure specific for directed networks is designed.

Inferring network topology from complex dynamics

Inferring the network topology from dynamical observations is a fundamental problem pervading research on complex systems. Here, we present a simple, direct method for inferring the structural connection topology of a network, given an observation of one collective dynamical trajectory. The general theoretical framework is applicable to arbitrary network dynamical systems described by ordinary differential equations. No interference (external driving) is required and the type of dynamics is hardly restricted in any way. In particular, the observed dynamics may be arbitrarily complex; stationary, invariant or transient; synchronous or asynchronous and chaotic or periodic. Presupposing a knowledge of the functional form of the dynamical units and of the coupling functions between them, we present an analytical solution to the inverse problem of finding the network topology from observing a time series of state variables only. Robust reconstruction is achieved in any sufficiently long generic observation of the system. We extend our method to simultaneously reconstructing both the entire network topology and all parameters appearing linear in the system's equations of motion. Reconstruction of network topology and system parameters is viable even in the presence of external noise that distorts the original dynamics substantially. The method provides a conceptually new step towards reconstructing a variety of real-world networks, including gene and protein interaction networks and neuronal circuits.

Using Small Molecules and Chemical Genetics To Interrogate Signaling Networks

The limited clinical success of therapeutics targeting cellular signaling processes is due to multiple factors, including off-target effects and complex feedback regulation encoded within the signaling network. To understand these effects, chemical proteomics and chemical genetics tools have been developed to map the direct targets of kinase inhibitors, determine the network-level response to inhibitor treatment, and to infer network topology. Here we provide an overview of chemical phosphoproteomic and chemical genetic methods, including specific examples where these methods have been applied to yield biological insight regarding network structure and the system-wide effects of targeted therapeutics. The challenges and caveats associated with each method are described, along with approaches being used to resolve some of these issues. With the broad array of available techniques the next decade should see a rapid improvement in our understanding of signaling networks regulation and response to targeted perturbations, leading to more efficacious therapeutic strategies.

From Pathways Databases to Network Models of Switching Behavior

The excitement in today's biology is driven by the huge amounts of information generated by high-throughput data-acquisition technologies, and by the expectation that these datasets will soon provide detailed understanding of life's processes. Ultimately, these datasets have to be integrated into a framework that facilitates the study of the dynamics arising from networks of physico–chemical interactions orchestrating the physiology of a biological cell. The bioinformatics community is actively responding to this call for integration in terms of frameworks of pathways databases [1,2]. This paper addresses the use of these databases as sources of dynamical models for biological phenomena. We focus here on models that are based on molecular interactions and how these interactions are coupled to explain observed cellular behavior. The model-building process that we describe below takes the point of view of a non-biologist who has access to online pathways databases but has not been directly involved in relevant experimental studies. Of course, one could argue that a better approach is for the modeler to collaborate with a biologist who is already familiar with the system and has developed intuition about how it works; in other words, the biologist may already have a “model” in mind—usually called a “hypothesis”—and what remains to be done is to encode this model in the language of mathematics. Note that this “hypothesis-driven” modeling approach already assumes a reduced network in the beginning of the modeling process. In contrast, we would like to show in this paper how a reduced network model is extracted from a much larger network, given a specific biological question and a set of relevant experimental observations. Mathematical models range from qualitative and probabilistic models to quantitative and deterministic kinetic models [3–5]. The chosen set of molecular interactions and processes form what we call a “network model.” Although the networks can have various degrees of detail, they all have the common property of being composed of nodes and edges representing interactions between nodes. Definitions of networks and pathways, as well as an example of a network model are given in the next section. Ultimately, we are interested in mechanistic models with well-defined molecular interactions or reaction mechanisms and corresponding rate equations that are subsequently solved numerically to simulate the phenomenon. Although mechanistic details are becoming available in increasing numbers of online pathways databases and knowledgebases, quantitative values of most kinetic parameters are still lacking—and this problem is compounded by the fact that many details of these pathways can be cell-specific (with regard to cell type, organism, etc.) and can have variability even among the same cell type in an organism. We provide below an overview of pathway resources on the Internet. Note that we are not concerned here with computational methods of determining or inferring network topology, or connectivity from omics data—on this topic the reader is referred to an article of Qi and Ge [3] that appeared in this journal recently. In this article, we illustrate how one extracts a reduced network model from a large preliminary network obtained from databases. The model extraction procedure is explained in the context of a specific biological question about a cell cycle checkpoint called the “restriction point” (R point)—that is, what is the smallest subset of interactions in the given network that can account for the switching behavior associated with this checkpoint? A method of qualitative network analysis is proposed to zoom into a core subnetwork which accounts for the essential qualitative behavior being modeled. Once the core network model is established, a kinetic model is constructed and a suite of mathematical analysis and computer programs can be used for further investigation.