2,832 research outputs found
Metrics for Graph Comparison: A Practitioner's Guide
Comparison of graph structure is a ubiquitous task in data analysis and
machine learning, with diverse applications in fields such as neuroscience,
cyber security, social network analysis, and bioinformatics, among others.
Discovery and comparison of structures such as modular communities, rich clubs,
hubs, and trees in data in these fields yields insight into the generative
mechanisms and functional properties of the graph.
Often, two graphs are compared via a pairwise distance measure, with a small
distance indicating structural similarity and vice versa. Common choices
include spectral distances (also known as distances) and distances
based on node affinities. However, there has of yet been no comparative study
of the efficacy of these distance measures in discerning between common graph
topologies and different structural scales.
In this work, we compare commonly used graph metrics and distance measures,
and demonstrate their ability to discern between common topological features
found in both random graph models and empirical datasets. We put forward a
multi-scale picture of graph structure, in which the effect of global and local
structure upon the distance measures is considered. We make recommendations on
the applicability of different distance measures to empirical graph data
problem based on this multi-scale view. Finally, we introduce the Python
library NetComp which implements the graph distances used in this work
Local versus Global Knowledge in the Barabasi-Albert scale-free network model
The scale-free model of Barabasi and Albert gave rise to a burst of activity
in the field of complex networks. In this paper, we revisit one of the main
assumptions of the model, the preferential attachment rule. We study a model in
which the PA rule is applied to a neighborhood of newly created nodes and thus
no global knowledge of the network is assumed. We numerically show that global
properties of the BA model such as the connectivity distribution and the
average shortest path length are quite robust when there is some degree of
local knowledge. In contrast, other properties such as the clustering
coefficient and degree-degree correlations differ and approach the values
measured for real-world networks.Comment: Revtex format. Final version appeared in PR
Hierarchy and assortativity as new tools for affinity investigation: the case of the TBA aptamer-ligand complex
Aptamers are single stranded DNA, RNA or peptide sequences having the ability
to bind a variety of specific targets (proteins, molecules as well as ions).
Therefore, aptamer production and selection for therapeutic and diagnostic
applications is very challenging. Usually they are in vitro generated, but,
recently, computational approaches have been developed for the in silico
selection, with a higher affinity for the specific target. Anyway, the
mechanism of aptamer-ligand formation is not completely clear, and not obvious
to predict. This paper aims to develop a computational model able to describe
aptamer-ligand affinity performance by using the topological structure of the
corresponding graphs, assessed by means of numerical tools such as the
conventional degree distribution, but also the rank-degree distribution
(hierarchy) and the node assortativity. Calculations are applied to the
thrombin binding aptamer (TBA), and the TBA-thrombin complex, produced in the
presence of Na+ or K+. The topological analysis reveals different affinity
performances between the macromolecules in the presence of the two cations, as
expected by previous investigations in literature. These results nominate the
graph topological analysis as a novel theoretical tool for testing affinity.
Otherwise, starting from the graphs, an electrical network can be obtained by
using the specific electrical properties of amino acids and nucleobases.
Therefore, a further analysis concerns with the electrical response, which
reveals that the resistance sensitively depends on the presence of sodium or
potassium thus posing resistance as a crucial physical parameter for testing
affinity.Comment: 12 pages, 5 figure
Multiplicative Attribute Graph Model of Real-World Networks
Large scale real-world network data such as social and information networks
are ubiquitous. The study of such social and information networks seeks to find
patterns and explain their emergence through tractable models. In most
networks, and especially in social networks, nodes have a rich set of
attributes (e.g., age, gender) associated with them.
Here we present a model that we refer to as the Multiplicative Attribute
Graphs (MAG), which naturally captures the interactions between the network
structure and the node attributes. We consider a model where each node has a
vector of categorical latent attributes associated with it. The probability of
an edge between a pair of nodes then depends on the product of individual
attribute-attribute affinities. The model yields itself to mathematical
analysis and we derive thresholds for the connectivity and the emergence of the
giant connected component, and show that the model gives rise to networks with
a constant diameter. We analyze the degree distribution to show that MAG model
can produce networks with either log-normal or power-law degree distributions
depending on certain conditions.Comment: 33 pages, 6 figure
Probing the Extent of Randomness in Protein Interaction Networks
Proteinâprotein interaction (PPI) networks are commonly explored for the identification of distinctive biological traits, such as pathways, modules, and functional motifs. In this respect, understanding the underlying network structure is vital to assess the significance of any discovered features. We recently demonstrated that PPI networks show degree-weighted behavior, whereby the probability of interaction between two proteins is generally proportional to the product of their numbers of interacting partners or degrees. It was surmised that degree-weighted behavior is a characteristic of randomness. We expand upon these findings by developing a random, degree-weighted, network model and show that eight PPI networks determined from single high-throughput (HT) experiments have global and local properties that are consistent with this model. The apparent random connectivity in HT PPI networks is counter-intuitive with respect to their observed degree distributions; however, we resolve this discrepancy by introducing a non-network-based model for the evolution of protein degrees or âbinding affinities.â This mechanism is based on duplication and random mutation, for which the degree distribution converges to a steady state that is identical to one obtained by averaging over the eight HT PPI networks. The results imply that the degrees and connectivities incorporated in HT PPI networks are characteristic of unbiased interactions between proteins that have varying individual binding affinities. These findings corroborate the observation that curated and high-confidence PPI networks are distinct from HT PPI networks and not consistent with a random connectivity. These results provide an avenue to discern indiscriminate organizations in biological networks and suggest caution in the analysis of curated and high-confidence networks
A simple physical model for scaling in protein-protein interaction networks
It has recently been demonstrated that many biological networks exhibit a
scale-free topology where the probability of observing a node with a certain
number of edges (k) follows a power law: i.e. p(k) ~ k^-g. This observation has
been reproduced by evolutionary models. Here we consider the network of
protein-protein interactions and demonstrate that two published independent
measurements of these interactions produce graphs that are only weakly
correlated with one another despite their strikingly similar topology. We then
propose a physical model based on the fundamental principle that (de)solvation
is a major physical factor in protein-protein interactions. This model
reproduces not only the scale-free nature of such graphs but also a number of
higher-order correlations in these networks. A key support of the model is
provided by the discovery of a significant correlation between number of
interactions made by a protein and the fraction of hydrophobic residues on its
surface. The model presented in this paper represents the first physical model
for experimentally determined protein-protein interactions that comprehensively
reproduces the topological features of interaction networks. These results have
profound implications for understanding not only protein-protein interactions
but also other types of scale-free networks.Comment: 50 pages, 17 figure
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