Bitcoin Transaction Networks: an overview of recent results

Vallarano, Nicolò; Tessone, Claudio; Squartini, Tiziano

doi:10.48550/arxiv.2005.00114

Cited by 1 publication

(1 citation statement)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Problems like these are usually affected by the issues of accuracy, speed and scalability: the present paper aims at addressing them at once, by comparing the performance of three algorithms, i.e. Newton's method, a quasi-Newton method and a recently-proposed fixedpoint recipe [22,23], to solve a variety of ERGMs, defined by binary and weighted constraints in both a directed and an undirected fashion.…”

Section: Introductionmentioning

confidence: 99%

Fast and scalable likelihood maximization for Exponential Random Graph Models with local constraints

Vallarano,

Bruno,

Marchese

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

Exponential Random Graph Models (ERGMs) have gained increasing popularity over the years. Rooted into statistical physics, the ERGMs framework has been successfully employed for reconstructing networks, detecting statistically significant patterns in graphs, counting networked configurations with given properties. From a technical point of view, the ERGMs workflow is defined by two subsequent optimization steps: the first one concerns the maximization of Shannon entropy and leads to identify the functional form of the ensemble probability distribution that is maximally non-committal with respect to the missing information; the second one concerns the maximization of the likelihood function induced by this probability distribution and leads to its numerical determination. This second step translates into the resolution of a system of O(N ) non-linear, coupled equations (with N being the total number of nodes of the network under analysis), a problem that is affected by three main issues, i.e. accuracy, speed and scalability. The present paper aims at addressing these problems by comparing the performance of three algorithms (i.e. Newton's method, a quasi-Newton method and a recently-proposed fixed-point recipe) in solving several ERGMs, defined by binary and weighted constraints in both a directed and an undirected fashion. While Newton's method performs best for relatively little networks, the fixed-point recipe is to be preferred when large configurations are considered, as it ensures convergence to the solution within seconds for networks with hundreds of thousands of nodes (e.g. the Internet, Bitcoin). We attach to the paper a Python code implementing the three aforementioned algorithms on all the ERGMs considered in the present work.

show abstract

Section: Introductionmentioning

confidence: 99%