scholarly journals Testing biological network motif significance with exponential random graph models

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Alex Stivala ◽  
Alessandro Lomi
Keyword(s):  
Random Graph ◽  
Biological Networks ◽  
Statistical Significance ◽  
Model Parameters ◽  
Ppi Network ◽  
Exponential Random Graph Models ◽  
Graph Models ◽  
Random Graph Models ◽  
Topological Features ◽  
Exponential Random Graph

AbstractAnalysis of the structure of biological networks often uses statistical tests to establish the over-representation of motifs, which are thought to be important building blocks of such networks, related to their biological functions. However, there is disagreement as to the statistical significance of these motifs, and there are potential problems with standard methods for estimating this significance. Exponential random graph models (ERGMs) are a class of statistical model that can overcome some of the shortcomings of commonly used methods for testing the statistical significance of motifs. ERGMs were first introduced into the bioinformatics literature over 10 years ago but have had limited application to biological networks, possibly due to the practical difficulty of estimating model parameters. Advances in estimation algorithms now afford analysis of much larger networks in practical time. We illustrate the application of ERGM to both an undirected protein–protein interaction (PPI) network and directed gene regulatory networks. ERGM models indicate over-representation of triangles in the PPI network, and confirm results from previous research as to over-representation of transitive triangles (feed-forward loop) in an E. coli and a yeast regulatory network. We also confirm, using ERGMs, previous research showing that under-representation of the cyclic triangle (feedback loop) can be explained as a consequence of other topological features.

Soft constraints: exponential random graph models

2017 ◽  
Author(s):  
A.C.C. Coolen ◽  
A. Annibale ◽  
E.S. Roberts
Keyword(s):  
Random Graph ◽  
Model Parameters ◽  
Soft Constraints ◽  
Star Model ◽  
Exponential Random Graph Models ◽  
Graph Models ◽  
Random Graph Models ◽  
Exponential Random Graph ◽  
Lagrange’S Method ◽  
Individual Node

Exponential random graph models (ERGMs) provide conceptually elegant recipes for generating soft-constrained random graphs. This chapter begins by explaining the theory and describing how to properly specify an ERGM, including demonstrating Lagrange’s method to derive the values of the model parameters that correspond to the desired constraints. Three ERGMs, all with constraints depending linearly on the adjacency matrix, are solved exactly: the targeted total number of links, targeted individual node degrees and targeted number of two-way links in a directed graph. However, when the controlled features become more complicated, ERGMs have a tendency to produce graphs in extreme phases (very dense or very sparse). The two-star model and the Strauss model are worked through in detail using advanced techniques from statistical mechanics in order to analyze the phase transitions. The chapter closes with a discussion of the strengths and weaknesses of ERGMs as null models.

scholarly journals Exponential random graph models for little networks

2021 ◽  
Vol 64 ◽  
pp. 225-238
Author(s):  
George G. Vega Yon ◽  
Andrew Slaughter ◽  
Kayla de la Haye
Keyword(s):  
Random Graph ◽  
Exponential Random Graph Models ◽  
Graph Models ◽  
Random Graph Models ◽  
Exponential Random Graph

scholarly journals The performance of permutations and exponential random graph models when analyzing animal networks

2020 ◽  
Vol 31 (5) ◽  
pp. 1266-1276 ◽  
Author(s):  
Julian C Evans ◽  
David N Fisher ◽  
Matthew J Silk
Keyword(s):  
Social Network ◽  
Random Graph ◽  
False Positive ◽  
False Negative ◽  
Error Rates ◽  
Network Data ◽  
Exponential Random Graph Models ◽  
Graph Models ◽  
Random Graph Models ◽  
Exponential Random Graph

Abstract Social network analysis is a suite of approaches for exploring relational data. Two approaches commonly used to analyze animal social network data are permutation-based tests of significance and exponential random graph models. However, the performance of these approaches when analyzing different types of network data has not been simultaneously evaluated. Here we test both approaches to determine their performance when analyzing a range of biologically realistic simulated animal social networks. We examined the false positive and false negative error rate of an effect of a two-level explanatory variable (e.g., sex) on the number and combined strength of an individual’s network connections. We measured error rates for two types of simulated data collection methods in a range of network structures, and with/without a confounding effect and missing observations. Both methods performed consistently well in networks of dyadic interactions, and worse on networks constructed using observations of individuals in groups. Exponential random graph models had a marginally lower rate of false positives than permutations in most cases. Phenotypic assortativity had a large influence on the false positive rate, and a smaller effect on the false negative rate for both methods in all network types. Aspects of within- and between-group network structure influenced error rates, but not to the same extent. In "grouping event-based" networks, increased sampling effort marginally decreased rates of false negatives, but increased rates of false positives for both analysis methods. These results provide guidelines for biologists analyzing and interpreting their own network data using these methods.

scholarly journals Bayesian exponential random graph models with nodal random effects

2016 ◽  
Vol 46 ◽  
pp. 11-28 ◽  
Author(s):  
S. Thiemichen ◽  
N. Friel ◽  
A. Caimo ◽  
G. Kauermann
Keyword(s):  
Random Effects ◽  
Random Graph ◽  
Exponential Random Graph Models ◽  
Graph Models ◽  
Random Graph Models ◽  
Exponential Random Graph
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