Lecture

Distances and Motif Counts

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

In course

MATH-448: Statistical analysis of network data

A first course in statistical network analysis and applications. ...

Description

This lecture by the instructor covers the definition of distances on graphs, including the edit distance and the Hamming distance. It explores the cut norm of graphs, the spanning tree dissimilarity, and the blockmodel. The lecture delves into metrics and norms, focusing on the Hamming distance, Jaccard distance, lp distances on eigenvalues, and the Steinhaus transform. It also discusses ERGMs, their applications in sociology, and the exponential random graph models. The content includes examples, definitions, theorems, and special cases related to network data analysis.

Instructor

Sofia Charlotta Olhede

I am a professor of Statistics at EPFL. I did my PhD in Mathematics at Imperial College London, and graduated in 2003. I was an assistant professor (lecturer) at Imperial College London 2002-2006, and an associate professor (senior lecturer) 2006-2007. In 2007 I moved to University College London and became a full professor. I moved to EPFL in 2019, and in 2018 I became an Institute of Mathematical Statistics Fellow with citation “For seminal contributions to the theory and application of large and heteroge

Official source

Ontological neighbourhood

Mathematics

Discrete mathematics: Graph theory

Related concepts (31)

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.

Levenshtein distance

In information theory, linguistics, and computer science, the Levenshtein distance is a string metric for measuring the difference between two sequences. Informally, the Levenshtein distance between two words is the minimum number of single-character edits (insertions, deletions or substitutions) required to change one word into the other. It is named after the Soviet mathematician Vladimir Levenshtein, who considered this distance in 1965.

Graph theory

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called links or lines). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics.

Glossary of graph theory

This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes or vertices connected in pairs by lines or edges.

Connectivity (graph theory)

In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more isolated subgraphs. It is closely related to the theory of network flow problems. The connectivity of a graph is an important measure of its resilience as a network. In an undirected graph G, two vertices u and v are called connected if G contains a path from u to v.

Related lectures (64)

Statistical analysis of network data

Covers stochastic properties, network structures, models, statistics, centrality measures, and sampling methods in network data analysis.

Graphical Models: Representing Probabilistic Distributions

Covers graphical models for probabilistic distributions using graphs, nodes, and edges.

Minimum Spanning Trees: Prim's Algorithm

Explores Prim's algorithm for minimum spanning trees and introduces the Traveling Salesman Problem.

Statistical Analysis of Network Data

Introduces network data structures, models, and analysis techniques, emphasizing permutation invariance and Erdős-Rényi networks.

Graph Theory and Network Flows

Introduces graph theory, network flows, and flow conservation laws with practical examples and theorems.