Efficient generation of large random networks (original) (raw)

Parallel Algorithms for Generating Random Networks with Given Degree Sequences

International Journal of Parallel Programming, 2015

Random networks are widely used for modeling and analyzing complex processes. Many mathematical models have been proposed to capture diverse real-world networks. One of the most important aspects of these models is degree distribution. Chung-Lu (CL) model is a random network model, which can produce networks with any given arbitrary degree distribution. The complex systems we deal with nowadays are growing larger and more diverse than ever. Generating random networks with any given degree distribution consisting of billions of nodes and edges or more has become a necessity, which requires efficient and parallel algorithms. We present an MPI-based distributed memory parallel algorithm for generating massive random networks using CL model, which takes O(m+n P + P) time with high probability and O(n) space per processor, where n, m, and P are the number of nodes, edges and processors, respectively. The time efficiency is achieved by using a novel load-balancing algorithm. Our algorithms scale very well to a large number of processors and can generate massive powerlaw networks with one billion nodes and 250 billion edges in one minute using 1024 processors.

Generating random networks by linear programming approaches

Social networks is a recent area of research motivated by the empirical study of real-world networks, such as social relations, protein interaction, neuronal connections, etc. As closed-form probabilistic models of networks are often not available, the ability of randomly generating networks verifying specific constraints might be useful. The purpose is to develop optimization-based procedures to randomly generate networks with structural constraints, within the probabilistic framework of conditional uniform models. Based on the characterization of families of networks by means of systems of linear constraints, polynomial-time methods to generate networks with specified structural properties are constructed. The computational results suggest that the proposed methods can represent a general framework for the efficient simulation of random networks even beyond the models analyzed in this Master Thesis.

Generating uniformly distributed random networks

2005

The analysis of real networks taken from the biological, social, and physical sciences often requires a carefully posed statistical null-hypothesis approach. One common method requires comparing real networks to an ensemble of random matrices that satisfy realistic constraints in which each different matrix member is equiprobable. We discuss existing methods for generating uniformly distributed ͑constrained͒ random matrices, describe their shortcomings, and present an efficient technique that should have many practical applications.

On Generating Random Network Structures: Trees

Lecture Notes in Computer Science, 2003

Random trees (RTs) are widely used for testing various algorithms on tree-type networks and also for generating connected graphs similar to real nets. While random topologies based on RTs are generally accepted as network models, the task of their generation is almost unexplored. In this paper we discuss the set of basic algorithms for generating random trees. The fast algorithms with proven properties are presented for generating random trees under conditions for given restrictions, such as a limited node degree, fixed node degrees, and different probabilities of edge existence. Generating random graphs similar to physical networks are underway.

Algorithms for generating large-scale clustered random graphs

Network Science, 2014

Real-world networks are often compared to random graphs to assess whether their topological structure could be a result of random processes. However, a simple random graph in large scale often lacks social structure beyond the dyadic level. As a result we need to generate clustered random graph to compare the local structure at higher network levels. In this paper a generalized version of Gleeson's algorithm G(VS, VT, ES, ET, S, T) is advanced to generate a clustered random graph in large-scale which persists the number of vertices |V|, the number of edges |E|, and the global clustering coefficient CΔ as in the real network and it works successfully for nine large-scale networks. Our new algorithm also has advantages in randomness evaluation and computation efficiency when compared with the existing algorithms.

Fast Generation of Large Scale Social Networks While Incorporating Transitive Closures

2012 International Conference on Privacy, Security, Risk and Trust and 2012 International Confernece on Social Computing, 2012

A key challenge in the social network community is the problem of network generation-that is, how can we create synthetic networks that match characteristics traditionally found in most real world networks? Important characteristics that are present in social networks include a power law degree distribution, small diameter, and large amounts of clustering. However, most current network generators, such as the Chung Lu and Kronecker models, largely ignore the clustering present in a graph and focus on preserving other network statistics, such as the power law distribution. Models such as the exponential random graph model have a transitivity parameter that can capture clustering, but they are computationally difficult to learn, making scaling to large real world networks intractable. In this work, we propose an extension to the Chung Lu random graph model, the Transitive Chung Lu (TCL) model, which incorporates the notion transitive edges. Specifically, it combines the standard Chung Lu model with edges that are formed through transitive closure (e.g., by connecting a 'friend of a friend'). We prove TCL's expected degree distribution is equal to the degree distribution of the original input graph, while still providing the ability to capture the clustering in the network. The single parameter required by our model can be learned in seconds on graphs with millions of edges; networks can be generated in time that is linear in the number of edges. We demonstrate the performance of TCL on four real-world social networks, including an email dataset with hundreds of thousands of nodes and millions of edges, showing TCL generates graphs that match the degree distribution, clustering coefficients and hop plots of the original networks.

Fast Generation of Spatially Embedded Random Networks

IEEE Transactions on Network Science and Engineering, 2017

Spatially Embedded Random Networks such as the Waxman random graph have been used in many settings for synthesizing networks. Prior to our work, there existed no software for generating these efficiently. Existing techniques are Oðn 2 Þ where n is the number of nodes in the network; in this paper we present an Oðn þ eÞ algorithm, where e is the number of edges.

The generation of random directed networks with prescribed 1-node and 2-node degree correlations

Journal of Physics A: Mathematical and Theoretical, 2008

The generation of random networks is a very common problem in complex network research. In this paper, we have studied the correlation nature of several real networks and found that, typically, a large number of links are deterministic, i.e. they cannot be randomized. This finding permits fast generation of ensembles of maximally random networks with prescribed 1-node and 2-node degree correlations. When the introduction of self-loops or multiple-links are not desired, random network generation methods typically reach blocked states. Here, a mechanism is proposed, the 'force-and-drop' method, to overcome such states. Our algorithm can be easily simplified for undirected graphs and reduced to account for any subclass of 2-node degree correlations.

Generating conditional uniform random networks by optimization procedures

Complex networks is a recent area of research motivated by the empirical study of realworld networks, such as social relations, protein interaction, neuronal connections, etc. As closed-form probabilistic models of networks are often not available, the ability of randomly generating networks verifying specific constraints might be useful. The purpose of this work is to develop optimization-based procedures to randomly generate networks with structural constraints, within the probabilistic framework of conditional uniform models. Based on the characterization of families of networks by means of systems of linear constraints, polynomialtime methods to generate networks with specified structural properties are constructed.

Generating network models using the S-metric

2008

The ability to create random models of real networks is useful for understanding the interactions in these systems. Several researchers have proposed modeling complex networks by using the node degree distribution, the most popular being a power-law distribution. Recent work by Li et al. introduced the S metric as a metric to characterize the structure of networks with power-law distributions. In this paper, we examine some of the practical difficulties of producing random graphs with a given degree sequence and an approximate S value. We give a solution for this problem that we have had success using in our research.