Using Subgraph Distributions for Characterizing Networks and Fitting Random Graph Models

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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Interplay between $$k$$-core and community structure in complex networks

Scientific Reports ◽

10.1038/s41598-020-71426-8 ◽

2020 ◽

Vol 10 (1) ◽

Author(s):

Irene Malvestio ◽

Alessio Cardillo ◽

Naoki Masuda

Keyword(s):

Community Structure ◽

Complex Networks ◽

Random Graph ◽

Shell Structure ◽

Crucial Role ◽

Configuration Model ◽

Graph Models ◽

Random Graph Models ◽

Empirical Networks

Abstract The organisation of a network in a maximal set of nodes having at least k neighbours within the set, known as $$k$$ k -core decomposition, has been used for studying various phenomena. It has been shown that nodes in the innermost $$k$$ k -shells play a crucial role in contagion processes, emergence of consensus, and resilience of the system. It is known that the $$k$$ k -core decomposition of many empirical networks cannot be explained by the degree of each node alone, or equivalently, random graph models that preserve the degree of each node (i.e., configuration model). Here we study the $$k$$ k -core decomposition of some empirical networks as well as that of some randomised counterparts, and examine the extent to which the $$k$$ k -shell structure of the networks can be accounted for by the community structure. We find that preserving the community structure in the randomisation process is crucial for generating networks whose $$k$$ k -core decomposition is close to the empirical one. We also highlight the existence, in some networks, of a concentration of the nodes in the innermost $$k$$ k -shells into a small number of communities.

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