724 research outputs found
Growing Graphs with Hyperedge Replacement Graph Grammars
Discovering the underlying structures present in large real world graphs is a
fundamental scientific problem. In this paper we show that a graph's clique
tree can be used to extract a hyperedge replacement grammar. If we store an
ordering from the extraction process, the extracted graph grammar is guaranteed
to generate an isomorphic copy of the original graph. Or, a stochastic
application of the graph grammar rules can be used to quickly create random
graphs. In experiments on large real world networks, we show that random
graphs, generated from extracted graph grammars, exhibit a wide range of
properties that are very similar to the original graphs. In addition to graph
properties like degree or eigenvector centrality, what a graph "looks like"
ultimately depends on small details in local graph substructures that are
difficult to define at a global level. We show that our generative graph model
is able to preserve these local substructures when generating new graphs and
performs well on new and difficult tests of model robustness.Comment: 18 pages, 19 figures, accepted to CIKM 2016 in Indianapolis, I
Generating realistic scaled complex networks
Research on generative models is a central project in the emerging field of
network science, and it studies how statistical patterns found in real networks
could be generated by formal rules. Output from these generative models is then
the basis for designing and evaluating computational methods on networks, and
for verification and simulation studies. During the last two decades, a variety
of models has been proposed with an ultimate goal of achieving comprehensive
realism for the generated networks. In this study, we (a) introduce a new
generator, termed ReCoN; (b) explore how ReCoN and some existing models can be
fitted to an original network to produce a structurally similar replica, (c)
use ReCoN to produce networks much larger than the original exemplar, and
finally (d) discuss open problems and promising research directions. In a
comparative experimental study, we find that ReCoN is often superior to many
other state-of-the-art network generation methods. We argue that ReCoN is a
scalable and effective tool for modeling a given network while preserving
important properties at both micro- and macroscopic scales, and for scaling the
exemplar data by orders of magnitude in size.Comment: 26 pages, 13 figures, extended version, a preliminary version of the
paper was presented at the 5th International Workshop on Complex Networks and
their Application
Kronecker Graphs: An Approach to Modeling Networks
How can we model networks with a mathematically tractable model that allows
for rigorous analysis of network properties? Networks exhibit a long list of
surprising properties: heavy tails for the degree distribution; small
diameters; and densification and shrinking diameters over time. Most present
network models either fail to match several of the above properties, are
complicated to analyze mathematically, or both. In this paper we propose a
generative model for networks that is both mathematically tractable and can
generate networks that have the above mentioned properties. Our main idea is to
use the Kronecker product to generate graphs that we refer to as "Kronecker
graphs".
First, we prove that Kronecker graphs naturally obey common network
properties. We also provide empirical evidence showing that Kronecker graphs
can effectively model the structure of real networks.
We then present KronFit, a fast and scalable algorithm for fitting the
Kronecker graph generation model to large real networks. A naive approach to
fitting would take super- exponential time. In contrast, KronFit takes linear
time, by exploiting the structure of Kronecker matrix multiplication and by
using statistical simulation techniques.
Experiments on large real and synthetic networks show that KronFit finds
accurate parameters that indeed very well mimic the properties of target
networks. Once fitted, the model parameters can be used to gain insights about
the network structure, and the resulting synthetic graphs can be used for null-
models, anonymization, extrapolations, and graph summarization
The Infinity Mirror Test for Graph Models
Graph models, like other machine learning models, have implicit and explicit
biases built-in, which often impact performance in nontrivial ways. The model's
faithfulness is often measured by comparing the newly generated graph against
the source graph using any number or combination of graph properties.
Differences in the size or topology of the generated graph therefore indicate a
loss in the model. Yet, in many systems, errors encoded in loss functions are
subtle and not well understood. In the present work, we introduce the Infinity
Mirror test for analyzing the robustness of graph models. This straightforward
stress test works by repeatedly fitting a model to its own outputs. A
hypothetically perfect graph model would have no deviation from the source
graph; however, the model's implicit biases and assumptions are exaggerated by
the Infinity Mirror test, exposing potential issues that were previously
obscured. Through an analysis of thousands of experiments on synthetic and
real-world graphs, we show that several conventional graph models degenerate in
exciting and informative ways. We believe that the observed degenerative
patterns are clues to the future development of better graph models.Comment: This was submitted to IEEE TKDE 2020, 12 pages and 8 figure
Synthetic generators for simulating social networks
An application area of increasing importance is creating agent-based simulations to model human societies. One component of developing these simulations is the ability to generate realistic human social networks. Online social networking websites, such as Facebook, Google+, and Twitter, have increased in popularity in the last decade. Despite the increase in online social networking tools and the importance of studying human behavior in these networks, collecting data directly from these networks is not always feasible due to privacy concerns. Previous work in this area has primarily been limited to 1) network generators that aim to duplicate a small subset of the original network\u27s properties and 2) problem-specific generators for applications such as the evaluation of community detection algorithms. In this thesis, we extended two synthetic network generators to enable them to duplicate the properties of a specific dataset. In the first generator, we consider feature similarity and label homophily among individuals when forming links. The second generator is designed to handle multiplex networks that contain different link types. We evaluate the performance of both generators on existing real-world social network datasets, as well as comparing our methods with a related synthetic network generator. In this thesis, we demonstrate that the proposed synthetic network generators are both time efficient and require only limited parameter optimization
- …