scholarly journals The Probability of Non-Existence of a Subgraph in a Moderately Sparse Random Graph

2018 ◽  
Vol 27 (4) ◽  
pp. 672-715
Author(s):  
DUDLEY STARK ◽  
NICK WORMALD
Keyword(s):  
Random Graph ◽  
General Procedure ◽  
Restricted Range ◽  
Graph Models ◽  
Random Graph Models ◽  
Wide Range ◽  
Applicable Range ◽  
The Common ◽  
Asymptotic Probability ◽  
Large Clusters

We develop a general procedure that finds recursions for statistics counting isomorphic copies of a graph G0 in the common random graph models ${\cal G}$(n,m) and ${\cal G}$(n,p). Our results apply when the average degrees of the random graphs are below the threshold at which each edge is included in a copy of G0. This extends an argument given earlier by the second author for G0=K3 with a more restricted range of average degree. For all strictly balanced subgraphs G0, our results give much information on the distribution of the number of copies of G0 that are not in large ‘clusters’ of copies. The probability that a random graph in ${\cal G}$(n,p) has no copies of G0 is shown to be given asymptotically by the exponential of a power series in n and p, over a fairly wide range of p. A corresponding result is also given for ${\cal G}$(n,m), which gives an asymptotic formula for the number of graphs with n vertices, m edges and no copies of G0, for the applicable range of m. An example is given, computing the asymptotic probability that a random graph has no triangles for p=o(n−7/11) in ${\cal G}$(n,p) and for m=o(n15/11) in ${\cal G}$(n,m), extending results of the second author.

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 Status and conservation of the giant muntjac Megamuntiacus vuquangensis, and notes on other muntjac species in Laos

Oryx ◽  
1998 ◽  
Vol 32 (1) ◽  
pp. 59-67 ◽  
Author(s):  
R. J. Timmins ◽  
T. D. Evans ◽  
Khamkhoun Khounboline ◽  
Chainoi Sisomphone
Keyword(s):  
Habitat Degradation ◽  
Range Limits ◽  
Restricted Range ◽  
Taxonomic Affinity ◽  
Red Data Book ◽  
Wide Range ◽  
Data Book ◽  
The Common ◽  
Near Future ◽  
Muntiacus Muntjak

The large-antlered, or giant, muntjac Megamuntiacus vuquangensis wasdescribed from Vietnam in 1994 and found concurrently in the Annamite Mountains and nearby hill ranges of central and southern Laos. The northerly and southerly range limits are still unknown. It may occupy a wide range of habitats and is found sympatrically with the common muntjac Muntiacus muntjak. Another muntjac species, the taxonomic affinity of which is as yet undetermined, was recently discovered to occur within its range. The large-antlered muntjac is probably not threatened with extinction in the near future, but in view of its restricted range and threats from habitat degradation and hunting, it should be classified as Vulnerable in the Red Data Book. Its future in Laos is largely dependent on the recently created protected-areas system to maintain large tracts of habitat and reduce hunting pressure.

Modularity in several random graph models

2017 ◽  
Vol 61 ◽  
pp. 947-953 ◽  
Author(s):  
Liudmila Ostroumova Prokhorenkova ◽  
Paweł Prałat ◽  
Andrei Raigorodskii
Keyword(s):  
Random Graph ◽  
Graph Models ◽  
Random Graph Models

scholarly journals Random graph models for directed acyclic networks

2009 ◽  
Vol 80 (4) ◽  
Author(s):  
Brian Karrer ◽  
M. E. J. Newman
Keyword(s):  
Random Graph ◽  
Graph Models ◽  
Random Graph Models

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.

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