Randomisation Algorithms for Large Sparse Matrices

  title={Randomisation Algorithms for Large Sparse Matrices},
  author={Kai Puolam{\"a}ki and Andreas Henelius and Antti Ukkonen},
  journal={Physical review. E},
  volume={99 5-1},
In many domains it is necessary to generate surrogate networks, e.g., for hypothesis testing of different properties of a network. Generating surrogate networks typically requires that different properties of the network are preserved, e.g., edges may not be added or deleted and edge weights may be restricted to certain intervals. In this paper we present an efficient property-preserving Markov chain Monte Carlo method termed CycleSampler for generating surrogate networks in which (1) edge… 

Figures and Tables from this paper



Analytical maximum-likelihood method to detect patterns in real networks

This work proposes a fast method that allows one to obtain expectation values and standard deviations of any topological property analytically across the entire graph ensemble, for any binary, weighted, directed or undirected network.

Constrained Randomisation of Weighted Networks

It is demonstrated that surrogate networks can provide additional information about network-specific characteristics and thus help interpreting empirical weighted networks.

Unbiased degree-preserving randomization of directed binary networks.

  • E. RobertsA. Coolen
  • Mathematics, Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2012
An ergodic detailed balance Markov chain with nontrivial acceptance probabilities for directed graphs is constructed, which converges to a strictly uniform measure and is based on edge swaps that conserve all in and out degrees.

Constrained Markovian Dynamics of Random Graphs

We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic

The null space problem II. Algorithms

This paper develops heuristic algorithms to find sparse null bases and shows how sparsest orthogonal null bases may be found for an $n-vector and a $t \times n$ dense matric by a divide and conquer strategy.

Community detection in graphs

Information and Influence Propagation in Social Networks

A detailed description of well-established diffusion models, including the independent cascade model and the linear threshold model, that have been successful at explaining propagation phenomena are described as well as numerous extensions to them, introducing aspects such as competition, budget, and time-criticality, among many others.

Assessing data mining results via swap randomization

For some datasets the structure discovered by the data mining algorithms is expected, given the row and column margins of the datasets, while for other datasets the discovered structure conveys information that is not captured by the margin counts.

xsample(): An R Function for Sampling Linear Inverse Problems

An R function is implemented that uses Markov chain Monte Carlo (MCMC) algorithms to uniformly sample the feasible region of constrained linear problems and a new algorithm where an MCMC step reflects on the inequality constraints.