50,238 research outputs found
Node Embedding over Temporal Graphs
In this work, we present a method for node embedding in temporal graphs. We
propose an algorithm that learns the evolution of a temporal graph's nodes and
edges over time and incorporates this dynamics in a temporal node embedding
framework for different graph prediction tasks. We present a joint loss
function that creates a temporal embedding of a node by learning to combine its
historical temporal embeddings, such that it optimizes per given task (e.g.,
link prediction). The algorithm is initialized using static node embeddings,
which are then aligned over the representations of a node at different time
points, and eventually adapted for the given task in a joint optimization. We
evaluate the effectiveness of our approach over a variety of temporal graphs
for the two fundamental tasks of temporal link prediction and multi-label node
classification, comparing to competitive baselines and algorithmic
alternatives. Our algorithm shows performance improvements across many of the
datasets and baselines and is found particularly effective for graphs that are
less cohesive, with a lower clustering coefficient
On Hardness of the Joint Crossing Number
The Joint Crossing Number problem asks for a simultaneous embedding of two
disjoint graphs into one surface such that the number of edge crossings
(between the two graphs) is minimized. It was introduced by Negami in 2001 in
connection with diagonal flips in triangulations of surfaces, and subsequently
investigated in a general form for small-genus surfaces. We prove that all of
the commonly considered variants of this problem are NP-hard already in the
orientable surface of genus 6, by a reduction from a special variant of the
anchored crossing number problem of Cabello and Mohar
The extremal genus embedding of graphs
Let Wn be a wheel graph with n spokes. How does the genus change if adding a
degree-3 vertex v, which is not in V (Wn), to the graph Wn? In this paper,
through the joint-tree model we obtain that the genus of Wn+v equals 0 if the
three neighbors of v are in the same face boundary of P(Wn); otherwise,
{\deg}(Wn + v) = 1, where P(Wn) is the unique planar embedding of Wn. In
addition, via the independent set, we provide a lower bound on the maximum
genus of graphs, which may be better than both the result of D. Li & Y. Liu and
the result of Z. Ouyang etc: in Europ. J. Combinatorics. Furthermore, we obtain
a relation between the independence number and the maximum genus of graphs, and
provide an algorithm to obtain the lower bound on the number of the distinct
maximum genus embedding of the complete graph Km, which, in some sense,
improves the result of Y. Caro and S. Stahl respectively
Reconstruction of graded groupoids from graded Steinberg algebras
We show how to reconstruct a graded ample Hausdorff groupoid with topologically principal
neutrally-graded component from the ring structure of its graded Steinberg algebra over
any commutative integral domain with 1, together with the embedding of the canonical
abelian subring of functions supported on the unit space. We deduce that
diagonal-preserving ring isomorphism of Leavitt path algebras implies -isomorphism
of -algebras for graphs and in which every cycle has an exit.
This is a joint work with Joan Bosa, Roozbeh Hazrat and Aidan Sims.Universidad de Málaga. Campus de Excelencia internacional AndalucÃa Tec
Multiple Network Embedding for Anomaly Detection in Time Series of Graphs
This paper considers the graph signal processing problem of anomaly detection
in time series of graphs. We examine two related, complementary inference
tasks: the detection of anomalous graphs within a time series, and the
detection of temporally anomalous vertices. We approach these tasks via the
adaptation of statistically principled methods for joint graph inference,
specifically multiple adjacency spectral embedding (MASE) and omnibus embedding
(OMNI). We demonstrate that these two methods are effective for our inference
tasks. Moreover, we assess the performance of these methods in terms of the
underlying nature of detectable anomalies. Our results delineate the relative
strengths and limitations of these procedures, and provide insight into their
use. Applied to a large-scale commercial search engine time series of graphs,
our approaches demonstrate their applicability and identify the anomalous
vertices beyond just large degree change.Comment: 22 pages, 11 figure
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