A Systematic Approach to Constructing Families of Incremental Topology Control Algorithms Using Graph Transformation

In the communication systems domain, constructing and maintaining network topologies via topology control (TC) algorithms is an important cross-cutting research area. Network topologies are usually modeled using attributed graphs whose nodes and edges represent the network nodes and their interconnecting links. A key requirement of TC algorithms is to fulfill certain consistency and optimization properties to ensure a high quality of service. Still, few attempts have been made to constructively integrate these properties into the development process of TC algorithms. Furthermore, even though many TC algorithms share substantial parts (such as structural patterns or tie-breaking strategies), few works constructively leverage these commonalities and differences of TC algorithms systematically. In previous work, we addressed the constructive integration of consistency properties into the development process. We outlined a constructive, model-driven methodology for designing individual TC algorithms. Valid and high-quality topologies are characterized using declarative graph constraints; TC algorithms are specified using programmed graph transformation. We applied a well-known static analysis technique to refine a given TC algorithm in a way that the resulting algorithm preserves the specified graph constraints. In this paper, we extend our constructive methodology by generalizing it to support the specification of families of TC algorithms. To show the feasibility of our approach, we reneging six existing TC algorithms and develop e-kTC, a novel energy-efficient variant of the TC algorithm kTC. Finally, we evaluate a subset of the specified TC algorithms using a new tool integration of the graph transformation tool eMoflon and the Simonstrator network simulation framework.Comment: Corresponds to the accepted manuscrip

Revealing Network Structure, Confidentially: Improved Rates for Node-Private Graphon Estimation

Motivated by growing concerns over ensuring privacy on social networks, we develop new algorithms and impossibility results for fitting complex statistical models to network data subject to rigorous privacy guarantees. We consider the so-called node-differentially private algorithms, which compute information about a graph or network while provably revealing almost no information about the presence or absence of a particular node in the graph. We provide new algorithms for node-differentially private estimation for a popular and expressive family of network models: stochastic block models and their generalization, graphons. Our algorithms improve on prior work, reducing their error quadratically and matching, in many regimes, the optimal nonprivate algorithm. We also show that for the simplest random graph models ($G(n,p)$ and $G(n,m)$), node-private algorithms can be qualitatively more accurate than for more complex models---converging at a rate of $\frac{1}{\epsilon^2 n^{3}}$ instead of $\frac{1}{\epsilon^2 n^2}$. This result uses a new extension lemma for differentially private algorithms that we hope will be broadly useful

Outlier Edge Detection Using Random Graph Generation Models and Applications

Outliers are samples that are generated by different mechanisms from other normal data samples. Graphs, in particular social network graphs, may contain nodes and edges that are made by scammers, malicious programs or mistakenly by normal users. Detecting outlier nodes and edges is important for data mining and graph analytics. However, previous research in the field has merely focused on detecting outlier nodes. In this article, we study the properties of edges and propose outlier edge detection algorithms using two random graph generation models. We found that the edge-ego-network, which can be defined as the induced graph that contains two end nodes of an edge, their neighboring nodes and the edges that link these nodes, contains critical information to detect outlier edges. We evaluated the proposed algorithms by injecting outlier edges into some real-world graph data. Experiment results show that the proposed algorithms can effectively detect outlier edges. In particular, the algorithm based on the Preferential Attachment Random Graph Generation model consistently gives good performance regardless of the test graph data. Further more, the proposed algorithms are not limited in the area of outlier edge detection. We demonstrate three different applications that benefit from the proposed algorithms: 1) a preprocessing tool that improves the performance of graph clustering algorithms; 2) an outlier node detection algorithm; and 3) a novel noisy data clustering algorithm. These applications show the great potential of the proposed outlier edge detection techniques.Comment: 14 pages, 5 figures, journal pape

Sampling random graph homomorphisms and applications to network data analysis

A graph homomorphism is a map between two graphs that preserves adjacency relations. We consider the problem of sampling a random graph homomorphism from a graph $F$ into a large network $\mathcal{G}$. We propose two complementary MCMC algorithms for sampling a random graph homomorphisms and establish bounds on their mixing times and concentration of their time averages. Based on our sampling algorithms, we propose a novel framework for network data analysis that circumvents some of the drawbacks in methods based on independent and neigborhood sampling. Various time averages of the MCMC trajectory give us various computable observables, including well-known ones such as homomorphism density and average clustering coefficient and their generalizations. Furthermore, we show that these network observables are stable with respect to a suitably renormalized cut distance between networks. We provide various examples and simulations demonstrating our framework through synthetic networks. We also apply our framework for network clustering and classification problems using the Facebook100 dataset and Word Adjacency Networks of a set of classic novels.Comment: 51 pages, 33 figures, 2 table