CS224w 01-intro

Network: Networks are a general language for describing complex systems of interacting entities.

Two types of Networks/Graphs:

Networks(also known as Natural Graphs):

Society; Communication system; Interactions between genes regulate life; thoughts

Information Graphs:

Information/knowledge are organized and linked

Scene graphs: how objects in a scene relate

Similarity networks: take data, connect similar points //相似网络

Sometimes the distinction is blurred

How are these systems organized? What are their design properties?

Behind many systems there is an intricate wiring diagram, a network, that defines the interactions between the components. We will never be able to model and predict these systems unless we understand the networks behind them.

Graphs: Machine Learning

How do we take advantage of relational structure for better prediction?

Complex domains(knowledge, text, images, etc.) have rich relational structure, which can be represented as a relational graph. By explocitly modeling relationships we achieve better performance.

Why Networks? Why Now?

Universal language for describing complex data

Shared bocabulary between fields

Data availability and computational challenges

Impact!

Ways to Analyze Networks

Predict the type/color of a given node: Node classification

Predict whether two nodes are linked: Link prediction

Identify densely linked clusters of nodes: Community detection

Measure similarity of two nodes/networks: Network similarly

Structure of Graphs

A network is a collection of objects where some pairs of objects are connected by links

Components of a Network

Objects: nodes, vertices \(N\)

Interactions:links,edges \(E\)

System:network,graph \(G(N,E)\)

Networks or Graphs?

Network often refers to real systems

Web, Social network, Metabolic network 代谢网络

Graph is a mathematical representation of a network

Web graphm, Social graph, Knowledge Graph

Language: Graph, vertex, edge

How do you define a network?

Choice of the proper network representation of a given domain/problem determines our ability to use networks successfully.

In some cases there is a unique, unambiguous representation

In other cases, the representation is by no means unique

The way you assign links will determine the nature of the question you can study

Choice of Network Representation

Directed vs. Undirected Graphs

Undirected

Links: undirected(symmetrical, reciprocal)

Directed

Links: directed(arcs)

Node Degrees

Complete Graph

Only undirected graph.

\(E_{max} = \frac{N(N-1)}{2}\)

An Undirected graph with the number of edges \(E = E_{max}\)is called a complete graph, and its average degree is \(N-1\)

Bipartite Graph

Bipartite Graph is a graph whose nodes can be divided into two disjoint sets \(U\) and \(V\)such that every link connects a node in \(U\)to one in \(V\); that is, \(U\) and \(V\) are independent sets.

Folded/Projected Bipartite Graphs

Reresenting Graphs: Adjacency Matrix

for a directed graph the matrix is not symmetric.

Adjacency Matrices are sparse

Representing Graphs: Adjacency list

Adjacency list:

Easier to work with if network is Large and Sparse.

Allow us to quickly retrieve all neighbors of a given node

Edge Attributes

possible options:

Weight;Ranking;Type;Sign;Properties depending on the structure of the rest of the graph: number of common friends

Bridge edge:If we erase the edge, the graph becomes disconnected

Articulation node: If we erase the node, the graph becomes disconnected

Connectivity of Directed Graphs

Strongly connected directed graph: has a path from each node to every other node and vice versa.

Weakly connected directed graph: is connected if we disregard the edge directions.