3,945 research outputs found
On the extremal properties of the average eccentricity
The eccentricity of a vertex is the maximum distance from it to another
vertex and the average eccentricity of a graph is the mean value
of eccentricities of all vertices of . The average eccentricity is deeply
connected with a topological descriptor called the eccentric connectivity
index, defined as a sum of products of vertex degrees and eccentricities. In
this paper we analyze extremal properties of the average eccentricity,
introducing two graph transformations that increase or decrease .
Furthermore, we resolve four conjectures, obtained by the system AutoGraphiX,
about the average eccentricity and other graph parameters (the clique number,
the Randi\' c index and the independence number), refute one AutoGraphiX
conjecture about the average eccentricity and the minimum vertex degree and
correct one AutoGraphiX conjecture about the domination number.Comment: 15 pages, 3 figure
ProtNN: Fast and Accurate Nearest Neighbor Protein Function Prediction based on Graph Embedding in Structural and Topological Space
Studying the function of proteins is important for understanding the
molecular mechanisms of life. The number of publicly available protein
structures has increasingly become extremely large. Still, the determination of
the function of a protein structure remains a difficult, costly, and time
consuming task. The difficulties are often due to the essential role of spatial
and topological structures in the determination of protein functions in living
cells. In this paper, we propose ProtNN, a novel approach for protein function
prediction. Given an unannotated protein structure and a set of annotated
proteins, ProtNN finds the nearest neighbor annotated structures based on
protein-graph pairwise similarities. Given a query protein, ProtNN finds the
nearest neighbor reference proteins based on a graph representation model and a
pairwise similarity between vector embedding of both query and reference
protein-graphs in structural and topological spaces. ProtNN assigns to the
query protein the function with the highest number of votes across the set of k
nearest neighbor reference proteins, where k is a user-defined parameter.
Experimental evaluation demonstrates that ProtNN is able to accurately classify
several datasets in an extremely fast runtime compared to state-of-the-art
approaches. We further show that ProtNN is able to scale up to a whole PDB
dataset in a single-process mode with no parallelization, with a gain of
thousands order of magnitude of runtime compared to state-of-the-art
approaches
Towards an Efficient Discovery of the Topological Representative Subgraphs
With the emergence of graph databases, the task of frequent subgraph
discovery has been extensively addressed. Although the proposed approaches in
the literature have made this task feasible, the number of discovered frequent
subgraphs is still very high to be efficiently used in any further exploration.
Feature selection for graph data is a way to reduce the high number of frequent
subgraphs based on exact or approximate structural similarity. However, current
structural similarity strategies are not efficient enough in many real-world
applications, besides, the combinatorial nature of graphs makes it
computationally very costly. In order to select a smaller yet structurally
irredundant set of subgraphs, we propose a novel approach that mines the top-k
topological representative subgraphs among the frequent ones. Our approach
allows detecting hidden structural similarities that existing approaches are
unable to detect such as the density or the diameter of the subgraph. In
addition, it can be easily extended using any user defined structural or
topological attributes depending on the sought properties. Empirical studies on
real and synthetic graph datasets show that our approach is fast and scalable
Pseudo-distance-regularised graphs are distance-regular or distance-biregular
The concept of pseudo-distance-regularity around a vertex of a graph is a
natural generalization, for non-regular graphs, of the standard
distance-regularity around a vertex. In this note, we prove that a
pseudo-distance-regular graph around each of its vertices is either
distance-regular or distance-biregular. By using a combinatorial approach, the
same conclusion was reached by Godsil and Shawe-Taylor for a distance-regular
graph around each of its vertices. Thus, our proof, which is of an algebraic
nature, can also be seen as an alternative demonstration of Godsil and
Shawe-Taylor's theorem
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