An Introductory Guide to Aligning Networks Using SANA, the Simulated Annealing Network Aligner.

Sequence alignment has had an enormous impact on our understanding of biology, evolution, and disease. The alignment of biological networks holds similar promise. Biological networks generally model interactions between biomolecules such as proteins, genes, metabolites, or mRNAs. There is strong evidence that the network topology-the "structure" of the network-is correlated with the functions performed, so that network topology can be used to help predict or understand function. However, unlike sequence comparison and alignment-which is an essentially solved problem-network comparison and alignment is an NP-complete problem for which heuristic algorithms must be used.Here we introduce SANA, the Simulated Annealing Network Aligner. SANA is one of many algorithms proposed for the arena of biological network alignment. In the context of global network alignment, SANA stands out for its speed, memory efficiency, ease-of-use, and flexibility in the arena of producing alignments between two or more networks. SANA produces better alignments in minutes on a laptop than most other algorithms can produce in hours or days of CPU time on large server-class machines. We walk the user through how to use SANA for several types of biomolecular networks

An introductory guide to aligning networks using SANA, the Simulated Annealing Network Aligner

Sequence alignment has had an enormous impact on our understanding of biology, evolution, and disease. The alignment of biological {\em networks} holds similar promise. Biological networks generally model interactions between biomolecules such as proteins, genes, metabolites, or mRNAs. There is strong evidence that the network topology -- the "structure" of the network -- is correlated with the functions performed, so that network topology can be used to help predict or understand function. However, unlike sequence comparison and alignment -- which is an essentially solved problem -- network comparison and alignment is an NP-complete problem for which heuristic algorithms must be used. Here we introduce SANA, the {\it Simulated Annealing Network Aligner}. SANA is one of many algorithms proposed for the arena of biological network alignment. In the context of global network alignment, SANA stands out for its speed, memory efficiency, ease-of-use, and flexibility in the arena of producing alignments between 2 or more networks. SANA produces better alignments in minutes on a laptop than most other algorithms can produce in hours or days of CPU time on large server-class machines. We walk the user through how to use SANA for several types of biomolecular networks. Availability: https://github.com/waynebhayes/SAN

Ergm.graphlets: A Package for ERG Modeling Based on Graphlet Statistics

Exponential-family random graph models are probabilistic network models that are parametrized by suffcient statistics based on structural (i.e., graph-theoretic) properties. The ergm package for the R statistical computing environment is a collection of tools for the analysis of network data within an exponential-family random graph model framework. Many difierent network properties can be employed as suffcient statistics for exponentialfamily random graph models by using the model terms fined in the ergm package; this functionality can be expanded by the creation of packages that code for additional network statistics. Here, our focus is on the addition of statistics based on graphlets. Graphlets are classes of small, connected, induced subgraphs that can be used to describe the topological structure of a network. We introduce an R package called ergm.graphlets that enables the use of graphlet properties of a network within the ergm package of R. The ergm.graphlets package provides a complete list of model terms that allows to incorporate statistics of any 2-, 3-, 4- and 5-node graphlets into exponential-family random graph models. The new model terms of the ergm.graphlets package enable both exponential-family random graph modeling of global structural properties and investigation of relationships between node attributes (i.e., covariates) and local topologies around nodes

Graphettes: Constant-time determination of graphlet and orbit identity including (possibly disconnected) graphlets up to size 8

Graphlets are small connected induced subgraphs of a larger graph $G$. Graphlets are now commonly used to quantify local and global topology of networks in the field. Methods exist to exhaustively enumerate all graphlets (and their orbits) in large networks as efficiently as possible using orbit counting equations. However, the number of graphlets in $G$ is exponential in both the number of nodes and edges in $G$. Enumerating them all is already unacceptably expensive on existing large networks, and the problem will only get worse as networks continue to grow in size and density. Here we introduce an efficient method designed to aid statistical sampling of graphlets up to size $k=8$ from a large network. We define graphettes as the generalization of graphlets allowing for disconnected graphlets. Given a particular (undirected) graphette $g$, we introduce the idea of the canonical graphette $\mathcal K(g)$ as a representative member of the isomorphism group $Iso(g)$ of $g$. We compute the mapping $\mathcal K$, in the form of a lookup table, from all $2^{k(k-1)/2}$ undirected graphettes $g$ of size $k\le 8$ to their canonical representatives $\mathcal K(g)$, as well as the permutation that transforms $g$ to $\mathcal K(g)$. We also compute all automorphism orbits for each canonical graphette. Thus, given any $k\le 8$ nodes in a graph $G$, we can in constant time infer which graphette it is, as well as which orbit each of the $k$ nodes belongs to. Sampling a large number $N$ of such $k$-sets of nodes provides an approximation of both the distribution of graphlets and orbits across $G$, and the orbit degree vector at each node.Comment: 13 pages, 4 figures, 2 tables. Accepted to PLOS ON

Network analysis of the NetHealth data: exploring co-evolution of individuals’ social network positions and physical activities

Abstract Understanding the relationship between individuals’ social networks and health could help devise public health interventions for reducing incidence of unhealthy behaviors or increasing prevalence of healthy ones. In this context, we explore the co-evolution of individuals’ social network positions and physical activities. We are able to do so because the NetHealth study at the University of Notre Dame has generated both high-resolution longitudinal social network (e.g., SMS) data and high-resolution longitudinal health-related behavioral (e.g., Fitbit physical activity) data. We examine trait differences between (i) users whose social network positions (i.e., centralities) change over time versus those whose centralities remain stable, (ii) users whose Fitbit physical activities change over time versus those whose physical activities remain stable, and (iii) users whose centralities and their physical activities co-evolve, i.e., correlate with each other over time. We find that centralities of a majority of all nodes change with time. These users do not show any trait difference compared to time-stable users. However, if out of all users whose centralities change with time we focus on those whose physical activities also change with time, then the resulting users are more likely to be introverted than time-stable users. Moreover, users whose centralities and physical activities both change with time and whose evolving centralities are significantly correlated (i.e., co-evolve) with evolving physical activities are more likely to be introverted as well as anxious compared to those users who are time-stable and do not have a co-evolution relationship. Our network analysis framework reveals several links between individuals’ social network structure, health-related behaviors, and the other (e.g., personality) traits. In the future, our study could lead to development of a predictive model of social network structure from behavioral/trait information and vice versa