Corpus ID: 36269487

On Hyperbolic Geometry Structure of Complex Networks Wenjie Fang Report of M 1 internship in

@inproceedings{Hu2011OnHG,
  title={On Hyperbolic Geometry Structure of Complex Networks Wenjie Fang Report of M 1 internship in},
  author={Guangda Hu and Michael Mahoney},
  year={2011}
}
Various real world phenomena can be modeled by a notion called complex network. Much effort has been devoted into understanding and manipulating this notion. Recent research hints that complex networks have an underlying hyperbolic geometry that gives them navigability, a highly desirable property observed in many complex networks. In this internship, a parameter called δ-hyperbolicity, which is related to the underlying hyperbolic geometry of a graph, is studied in contrast of navigability… Expand

Figures from this paper

Core–periphery models for graphs based on their δ-hyperbolicity: An example using biological networks
TLDR
The eccentricity-based bending property is introduced which is exploited to identify the core vertices of a graph by proposing two models: the maximum-peak model and the minimum cover set model and some new theorems are included, as well as proofs of the theorem proposed in the conference paper. Expand
Hyperbolicity Measures "Democracy" in Real-World Networks
TLDR
This work analyzes the hyperbolicity of real-world networks, a geometric quantity that measures if a space is negatively curved, and outlines an "influence area" for the vertices in the graph. Expand
On Computing the Hyperbolicity of Real-World Graphs
TLDR
This paper provides a new and more efficient algorithm, allowing, for the first time, the computation of the hyperbolicity of graphs with up to 200,000 nodes, and experimentally shows that it drastically outperforms the best previously available algorithms. Expand
An Investigation into Graph Curvature's Ability to Measure Congestion in Network Flow
A recent trend in network research involves finding the appropriate geometric model for a given network, and to use features of the model to infer information about the network. One piece ofExpand
Metric properties of large graphs
Large scale communication networks are everywhere, ranging from data centers withmillions of servers to social networks with billions of users. This thesis is devoted tothe fine-grained complexityExpand
Into the Square: On the Complexity of Some Quadratic-time Solvable Problems
TLDR
A web of Karp reductions is constructed, proving that a truly subquadratic-time algorithm for any of the problems in the web falsifies SETH, unless the well known Strong Exponential Time Hypothesis (in short, SETH) is false. Expand

References

SHOWING 1-10 OF 24 REFERENCES
Hyperbolic Geometry of Complex Networks
TLDR
It is shown that targeted transport processes without global topology knowledge are maximally efficient, according to all efficiency measures, in networks with strongest heterogeneity and clustering, and that this efficiency is remarkably robust with respect to even catastrophic disturbances and damages to the network structure. Expand
Algorithms on negatively curved spaces
TLDR
This work gives efficient algorithms and data structures for problems like approximate nearest-neighbor search and compact, low-stretch routing on subsets of negatively curved spaces of fixed dimension (including Hd as a special case). Expand
Complex networks: Structure and dynamics
Coupled biological and chemical systems, neural networks, social interacting species, the Internet and the World Wide Web, are only a few examples of systems composed by a large number of highlyExpand
Navigation in small-world networks: a scale-free continuum model
The small-world phenomenon, the principle that we are all linked by a short chain of intermediate acquaintances, has been investigated in mathematics and social sciences. It has been shown to beExpand
Analyzing Kleinberg's (and other) small-world Models
TLDR
The properties of Small-World networks, where links are much more likely to connect "neighbor nodes" than distant nodes, are analyzed, and expected θ(log n) diameter results for higher dimensional grids, as well as settings with less uniform base structures. Expand
Notes on diameters, centers, and approximating trees of delta-hyperbolic geodesic spaces and graphs
TLDR
This work provides a simple construction of distance approximating trees of δ-hyperbolic graphs G on n vertices with an additive error O(δ log 2 n) comparable with that given by M. Gromov. Expand
Hyperbolic embedding of internet graph for distance estimation and overlay construction
TLDR
It is found that if the curvature, that defines the extend of the bending, is selected in the adequate range, the accuracy of Internet distance embedding can be improved, and a new efficient centralized embedding algorithm is presented that enables the accurate embedding of short distances. Expand
Emergence of scaling in random networks
TLDR
A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems. Expand
Treewidth and Hyperbolicity of the Internet
TLDR
The tree width of the Internet appears to be quite large and being far from a tree with that respect, reflecting some high degree of connectivity, which proves the existence of a well linked core in the Internet. Expand
Distance Labeling in Hyperbolic Graphs
TLDR
This paper constructs a distance labeling scheme for bounded hyperbolicity graphs, that is a vertex labeling such that the distance between any two vertices of G can be estimated from their labels, without any other source of information. Expand
...
1
2
3
...