1. Models of networks
   1. Relationships
      1. Links
      2. Edges
         1. Directed edges
         2. Undirected edges
      3. Types
         1. Symmetric
         2. Asymmetric
   2. Collection of items
      1. Objects
      2. Nodes
         1. Neighbors
            1. Connected by an edge
   3. Mathematical models of network structures
   4. Immaterial
      1. Actual places
      2. Layout
   5. Is there a connection?
      1. Physically
      2. Logically
   6. Network structure
2. Paths and Connectivity
   1. Paths
      1. From node to node
         1. Sequence of nodes
         2. Connected by an edge
      2. Repeat nodes?
         1. Yes: Simple path
         2. No: Non simple path
      3. Cycles
         1. Path
         2. At least three edges
         3. First and last nodes are the same
         4. Allow redundancy
            1. Alternative routings
      4. How long a path is?
         1. Number of hops to travel
         2. Length of a path
            1. Number of steps
            2. Number of edges
            3. Sequence
            4. From
            5. Begining
            6. End
         3. Distance between two nodes
            1. Lenth of the shortest path between them
            2. Arranges nodes based
            3. Their distances
            4. From a fixed starting point
            5. Discover nodes layer by layer
         4. Breadth-first search
            1. Systematic method to determine distances
            2. From a starting node
            3. Reaches the closest nodes first
            4. Algorithm
            5. Declare all of your actual friends: Distance 1
            6. Find all their friends: Distance 2
            7. Find all of their friends: Distance 3
            8. Conditions
            9. Have not already been discovered in earlier layers
            10. Have an edge to some node in previous layer
   2. Can every node reach other node by a path?
      1. Connected
         1. Communication networks
         2. Transportation networks
         3. Move traffic from onw node to another
      2. Disconnected
         1. Social networks
      3. The small world phenomenon
         1. Connecting people around the globe
         2. Paths surprisingly short
         3. Reach almost anyone else
         4. Six degrees of separation
3. Components
   1. Connected component
   2. Dividing graphs into components
      1. Graph structure
      2. Internal structure
   3. Densely connected regions
   4. Giant components
      1. Connected component
      2. Significant fraction of all the nodes
      3. Consequences on mergers
4. Network datasets
   1. Reasons to use them
      1. Actual domain it comes from
      2. Use the dataset as a proxy for a related network
      3. Look for network properties
   2. Large data sources
   3. Data already meassured for us
   4. Main sources
      1. Collaboration graphs
         1. Who works with whom
         2. Specific settings
      2. Who talks to whom graphs
         1. Nodes
            1. Customers
            2. Employees
            3. Students
      3. Information linkage graphs
      4. Technological networks
      5. Networks in the natural world