Understanding network structure and having access to realistic graphs plays a central role in computer and social networks research. In this paper, we propose a complete, practical methodology for generating graphs that resemble a real graph of interest. The metrics of the original topology we target to match are the joint degree distribution (JDD) and the degree-dependent average clustering coefficient (c(k)). We start by developing efficient estimators for these two metrics based on a node sample collected via either independence sampling or random walks. Then, we process the output of the estimators to ensure that the target metrics are realizable. Finally, we propose an efficient algorithm for generating topologies that have the exact target JDD and a c(k) close to the target. Extensive simulations using real-life graphs show that the graphs generated by our methodology are similar to the original graph with respect to, not only the two target metrics, but also a wide range of other topological metrics. Furthermore, our generator is order of magnitudes faster than state-of-the-art techniques. © 2013 IEEE.

Exponential-family random graph models are probabilistic network models that are parametrized by suffcient statistics based on structural (i.e., graph-theoretic) properties. The ergm package for the R statistical computing environment is a collection of tools for the analysis of network data within an exponential-family random graph model framework. Many difierent network properties can be employed as suffcient statistics for exponentialfamily random graph models by using the model terms fined in the ergm package; this functionality can be expanded by the creation of packages that code for additional network statistics. Here, our focus is on the addition of statistics based on graphlets. Graphlets are classes of small, connected, induced subgraphs that can be used to describe the topological structure of a network. We introduce an R package called ergm.graphlets that enables the use of graphlet properties of a network within the ergm package of R. The ergm.graphlets package provides a complete list of model terms that allows to incorporate statistics of any 2-, 3-, 4- and 5-node graphlets into exponential-family random graph models. The new model terms of the ergm.graphlets package enable both exponential-family random graph modeling of global structural properties and investigation of relationships between node attributes (i.e., covariates) and local topologies around nodes.

We consider the problem of inferring the topology of a network with M sources and N receivers (an M -by-N network), by sending probes between the sources and receivers. Prior work has shown that this problem can be decomposed into two parts: first, infer smaller subnetwork components (1-by-N 's or 2-by-2's) and then merge them to identify the M -by-N topology. We focus on the second part, which had previously received less attention in the literature. We assume that a 1-by-N topology is given and that all 2-by-2 components can be queried and learned using end-to-end probes. The problem is which 2-by-2's to query and how to merge them with the given 1-by-N, so as to exactly identify the 2-by-N topology, and optimize a number of performance metrics, including the number of queries (which directly translates into measurement bandwidth), time complexity, and memory usage. We provide a lower bound, [N], on the number of 2-by-2's required by any active learning algorithm and propose two greedy algorithms. The first algorithm follows the framework of multiple hypothesis testing, in particular Generalized Binary Search (GBS). The second algorithm is called the Receiver Elimination Algorithm (REA) and follows a bottom-up approach. It requires exactly N-1 steps, which is much less than all N possible 2-by-2's. Simulation results demonstrate that both algorithms correctly identify the 2-by-N topology and are near-optimal, but REA is more efficient in practice. © 1991-2012 IEEE.