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Publication# Modeling Network Populations via Graph Distances

Abstract

This article introduces a new class of models for multiple networks. The core idea is to parameterize a distribution on labeled graphs in terms of a Frechet mean graph (which depends on a user-specified choice of metric or graph distance) and a parameter that controls the concentration of this distribution about its mean. Entropy is the natural parameter for such control, varying from a point mass concentrated on the Frechet mean itself to a uniform distribution over all graphs on a given vertex set. We provide a hierarchical Bayesian approach for exploiting this construction, along with straightforward strategies for sampling from the resultant posterior distribution. We conclude by demonstrating the efficacy of our approach via simulation studies and two multiple-network data analysis examples: one drawn from systems biology and the other from neuroscience. This article has online.

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Parameter

A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc. Parameter has more specific meanings within various disciplines, including mathematics, computer programming, engineering, statistics, logic, linguistics, and electronic musical composition.

Article (grammar)

An article is any member of a class of dedicated words that are used with noun phrases to mark the identifiability of the referents of the noun phrases. The category of articles constitutes a part of speech. In English, both "the" and "a(n)" are articles, which combine with nouns to form noun phrases. Articles typically specify the grammatical definiteness of the noun phrase, but in many languages, they carry additional grammatical information such as gender, number, and case.

Distance (graph theory)

In the mathematical field of graph theory, the distance between two vertices in a graph is the number of edges in a shortest path (also called a graph geodesic) connecting them. This is also known as the geodesic distance or shortest-path distance. Notice that there may be more than one shortest path between two vertices. If there is no path connecting the two vertices, i.e., if they belong to different connected components, then conventionally the distance is defined as infinite.

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