58 research outputs found
Emergence of Symmetry in Complex Networks
Many real networks have been found to have a rich degree of symmetry, which
is a very important structural property of complex network, yet has been rarely
studied so far. And where does symmetry comes from has not been explained. To
explore the mechanism underlying symmetry of the networks, we studied
statistics of certain local symmetric motifs, such as symmetric bicliques and
generalized symmetric bicliques, which contribute to local symmetry of
networks. We found that symmetry of complex networks is a consequence of
similar linkage pattern, which means that nodes with similar degree tend to
share similar linkage targets. A improved version of BA model integrating
similar linkage pattern successfully reproduces the symmetry of real networks,
indicating that similar linkage pattern is the underlying ingredient that
responsible for the emergence of the symmetry in complex networks.Comment: 7 pages, 7 figure
Symmetry based Structure Entropy of Complex Networks
Precisely quantifying the heterogeneity or disorder of a network system is
very important and desired in studies of behavior and function of the network
system. Although many degree-based entropies have been proposed to measure the
heterogeneity of real networks, heterogeneity implicated in the structure of
networks can not be precisely quantified yet. Hence, we propose a new structure
entropy based on automorphism partition to precisely quantify the structural
heterogeneity of networks. Analysis of extreme cases shows that entropy based
on automorphism partition can quantify the structural heterogeneity of networks
more precisely than degree-based entropy. We also summarized symmetry and
heterogeneity statistics of many real networks, finding that real networks are
indeed more heterogenous in the view of automorphism partition than what have
been depicted under the measurement of degree based entropies; and that
structural heterogeneity is strongly negatively correlated to symmetry of real
networks.Comment: 7 pages, 6 figure
Algebraic and Topological Indices of Molecular Pathway Networks in Human Cancers
Protein-protein interaction networks associated with diseases have gained
prominence as an area of research. We investigate algebraic and topological
indices for protein-protein interaction networks of 11 human cancers derived
from the Kyoto Encyclopedia of Genes and Genomes (KEGG) database. We find a
strong correlation between relative automorphism group sizes and topological
network complexities on the one hand and five year survival probabilities on
the other hand. Moreover, we identify several protein families (e.g. PIK, ITG,
AKT families) that are repeated motifs in many of the cancer pathways.
Interestingly, these sources of symmetry are often central rather than
peripheral. Our results can aide in identification of promising targets for
anti-cancer drugs. Beyond that, we provide a unifying framework to study
protein-protein interaction networks of families of related diseases (e.g.
neurodegenerative diseases, viral diseases, substance abuse disorders).Comment: 15 pages, 4 figure
Evolutionary Algorithms for Community Detection in Continental-Scale High-Voltage Transmission Grids
Symmetry is a key concept in the study of power systems, not only because the admittance and Jacobian matrices used in power flow analysis are symmetrical, but because some previous studies have shown that in some real-world power grids there are complex symmetries. In order to investigate the topological characteristics of power grids, this paper proposes the use of evolutionary algorithms for community detection using modularity density measures on networks representing supergrids in order to discover densely connected structures. Two evolutionary approaches (generational genetic algorithm, GGA+, and modularity and improved genetic algorithm, MIGA) were applied. The results obtained in two large networks representing supergrids (European grid and North American grid) provide insights on both the structure of the supergrid and the topological differences between different regions. Numerical and graphical results show how these evolutionary approaches clearly outperform to the well-known Louvain modularity method. In particular, the average value of modularity obtained by GGA+ in the European grid was 0.815, while an average of 0.827 was reached in the North American grid. These results outperform those obtained by MIGA and Louvain methods (0.801 and 0.766 in the European grid and 0.813 and 0.798 in the North American grid, respectively)
Dimensionality reduction and spectral properties of multilayer networks
Network representations are useful for describing the structure of a large
variety of complex systems. Although most studies of real-world networks
suppose that nodes are connected by only a single type of edge, most natural
and engineered systems include multiple subsystems and layers of connectivity.
This new paradigm has attracted a great deal of attention and one fundamental
challenge is to characterize multilayer networks both structurally and
dynamically. One way to address this question is to study the spectral
properties of such networks. Here, we apply the framework of graph quotients,
which occurs naturally in this context, and the associated eigenvalue
interlacing results, to the adjacency and Laplacian matrices of undirected
multilayer networks. Specifically, we describe relationships between the
eigenvalue spectra of multilayer networks and their two most natural quotients,
the network of layers and the aggregate network, and show the dynamical
implications of working with either of the two simplified representations. Our
work thus contributes in particular to the study of dynamical processes whose
critical properties are determined by the spectral properties of the underlying
network.Comment: minor changes; pre-published versio
Correlation of Automorphism Group Size and Topological Properties with Program-size Complexity Evaluations of Graphs and Complex Networks
We show that numerical approximations of Kolmogorov complexity (K) applied to
graph adjacency matrices capture some group-theoretic and topological
properties of graphs and empirical networks ranging from metabolic to social
networks. That K and the size of the group of automorphisms of a graph are
correlated opens up interesting connections to problems in computational
geometry, and thus connects several measures and concepts from complexity
science. We show that approximations of K characterise synthetic and natural
networks by their generating mechanisms, assigning lower algorithmic randomness
to complex network models (Watts-Strogatz and Barabasi-Albert networks) and
high Kolmogorov complexity to (random) Erdos-Renyi graphs. We derive these
results via two different Kolmogorov complexity approximation methods applied
to the adjacency matrices of the graphs and networks. The methods used are the
traditional lossless compression approach to Kolmogorov complexity, and a
normalised version of a Block Decomposition Method (BDM) measure, based on
algorithmic probability theory.Comment: 15 2-column pages, 20 figures. Forthcoming in Physica A: Statistical
Mechanics and its Application
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