370 research outputs found
An O(m) Algorithm for Cores Decomposition of Networks
The structure of large networks can be revealed by partitioning them to
smaller parts, which are easier to handle. One of such decompositions is based
on --cores, proposed in 1983 by Seidman. In the paper an efficient, ,
is the number of lines, algorithm for determining the cores decomposition
of a given network is presented
Short Cycles Connectivity
Short cycles connectivity is a generalization of ordinary connectivity.
Instead by a path (sequence of edges), two vertices have to be connected by a
sequence of short cycles, in which two adjacent cycles have at least one common
vertex. If all adjacent cycles in the sequence share at least one edge, we talk
about edge short cycles connectivity.
It is shown that the short cycles connectivity is an equivalence relation on
the set of vertices, while the edge short cycles connectivity components
determine an equivalence relation on the set of edges. Efficient algorithms for
determining equivalence classes are presented.
Short cycles connectivity can be extended to directed graphs (cyclic and
transitive connectivity). For further generalization we can also consider
connectivity by small cliques or other families of graphs
Corrected overlap weight and clustering coefficient
We discuss two well known network measures: the overlap weight of an edge and
the clustering coefficient of a node. For both of them it turns out that they
are not very useful for data analytic task to identify important elements
(nodes or links) of a given network. The reason for this is that they attain
their largest values on maximal subgraphs of relatively small size that are
more probable to appear in a network than that of larger size. We show how the
definitions of these measures can be corrected in such a way that they give the
expected results. We illustrate the proposed corrected measures by applying
them on the US Airports network using the program Pajek.Comment: The paper is a detailed and extended version of the talk presented at
the CMStatistics (ERCIM) 2015 Conferenc
Querying Probabilistic Neighborhoods in Spatial Data Sets Efficiently
In this paper we define the notion
of a probabilistic neighborhood in spatial data: Let a set of points in
, a query point , a distance metric \dist,
and a monotonically decreasing function be
given. Then a point belongs to the probabilistic neighborhood of with respect to with probability f(\dist(p,q)). We envision
applications in facility location, sensor networks, and other scenarios where a
connection between two entities becomes less likely with increasing distance. A
straightforward query algorithm would determine a probabilistic neighborhood in
time by probing each point in .
To answer the query in sublinear time for the planar case, we augment a
quadtree suitably and design a corresponding query algorithm. Our theoretical
analysis shows that -- for certain distributions of planar -- our algorithm
answers a query in time with high probability
(whp). This matches up to a logarithmic factor the cost induced by
quadtree-based algorithms for deterministic queries and is asymptotically
faster than the straightforward approach whenever .
As practical proofs of concept we use two applications, one in the Euclidean
and one in the hyperbolic plane. In particular, our results yield the first
generator for random hyperbolic graphs with arbitrary temperatures in
subquadratic time. Moreover, our experimental data show the usefulness of our
algorithm even if the point distribution is unknown or not uniform: The running
time savings over the pairwise probing approach constitute at least one order
of magnitude already for a modest number of points and queries.Comment: The final publication is available at Springer via
http://dx.doi.org/10.1007/978-3-319-44543-4_3
Degree Landscapes in Scale-Free Networks
We generalize the degree-organizational view of real-world networks with
broad degree-distributions in a landscape analogue with mountains (high-degree
nodes) and valleys (low-degree nodes). For example, correlated degrees between
adjacent nodes corresponds to smooth landscapes (social networks), hierarchical
networks to one-mountain landscapes (the Internet), and degree-disassortative
networks without hierarchical features to rough landscapes with several
mountains. We also generate ridge landscapes to model networks organized under
constraints imposed by the space the networks are embedded in, associated to
spatial or, in molecular networks, to functional localization. To quantify the
topology, we here measure the widths of the mountains and the separation
between different mountains.Comment: 4 pages, 5 figure
S3G2: a Scalable Structure-correlated Social Graph Generator
Benchmarking graph-oriented database workloads and graph-oriented database systems are increasingly becoming relevant in analytical Big Data tasks, such as social network analysis. In graph data, structure is not mainly found inside the nodes, but especially in the way nodes happen to be connected, i.e. structural correlations. Because such structural correlations determine join fan-outs experienced by graph analysis algorithms and graph query executors, they are an essential, yet typically neglected, ingredient of synthetic graph generators. To address this, we present S3G2: a Scalable Structure-correlated Social Graph Generator. This graph generator creates a synthetic social graph, containing non-uniform value distributions and structural correlations, and is intended as a testbed for scalable graph analysis algorithms and graph database systems. We generalize the problem to decompose correlated graph generation in multiple passes that each focus on one so-called "correlation dimension"; each of which can be mapped to a MapReduce task. We show that using S3G2 can generate social graphs that (i) share well-known graph connectivity characteristics typically found in real social graphs (ii) contain certain plausible structural correlations that influence the performance of graph analysis algorithms and queries, and (iii) can be quickly generated at huge sizes on common cluster hardware
A New Analysis Method for Simulations Using Node Categorizations
Most research concerning the influence of network structure on phenomena
taking place on the network focus on relationships between global statistics of
the network structure and characteristic properties of those phenomena, even
though local structure has a significant effect on the dynamics of some
phenomena. In the present paper, we propose a new analysis method for phenomena
on networks based on a categorization of nodes. First, local statistics such as
the average path length and the clustering coefficient for a node are
calculated and assigned to the respective node. Then, the nodes are categorized
using the self-organizing map (SOM) algorithm. Characteristic properties of the
phenomena of interest are visualized for each category of nodes. The validity
of our method is demonstrated using the results of two simulation models. The
proposed method is useful as a research tool to understand the behavior of
networks, in particular, for the large-scale networks that existing
visualization techniques cannot work well.Comment: 9 pages, 8 figures. This paper will be published in Social Network
Analysis and Mining(www.springerlink.com
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