# Today's assignment

Social structure. Read Preface, p. 1, and sections 1.1 to 1.3.2. Graph theory exercise due (distributed by email) - submit answers via the Moodle (see above for instructions regarding network diagrams). Brainstorm some MCSN examples with research questions.

# Question of the day

• How does a new musical trend (song, artist, style, genre) spread? (diffusion phenomenon)
• What sorts of questions (naive) might we like to answer about such a phenomenon?
• How could musical diffusion be modelled with SNA?
• What sorts of research methods could be applied?

# Technical details

• Any questions on using the Moodle?
• Any problems with Pajek? Issues with Wine?
• Were you able to obtain and open the Pajek datasets?
• Note that Pajek help exists!

• Reading: Sections 1.1 to 1.3.2. - dining table partners data
• Examine the data file in a text editor (note: be careful not to save as anything but "plain text"!)
• Manipulate the network using Pajek (change reciprocated choices into edges)
• Manipulate the data using a text editor (add another person to the data)
• Create a new network from scratch
• Visualize the network in various ways using the Layout command (rotate in 3D using x y z X Y Z keys.)
• Playing around with Pajek will help you understand both SNA and Pajek...and it's kind of fun!

# Graph theory (Wilson ch. 1)

• vertex
• edge,arc
• degree
• graph, digraph
• multiple edges, loops
• simple graph
• walk (alternating sequence of connected vertices and lines)
• path (alternating sequence of connected vertices and lines, such that the vertices don't repeat)
• Eulerian graph (contains a walk containing every edge once, and returning to starting point)
• Hamiltonian graph (contains a walk containing every vertex once, and returning to starting point)
• connected and disconnected graphs
• tree (only one path between each pair of vertices)
• planar graph
• counting graphs
• isomorphic graphs, and difference
• two graphs are isomorphic if we can pair their vertices (from one graph to the other), such that when two vertices are connected in one graph, their pairs are connected in the other.
• when vertices are not labelled, isomorphic graphs are identical - no difference!
• how many different simple graphs can you create with a fixed number of vertices? (1,2,3,4,5...). (click here for some rather surprising answers to this question, considering graphs of up to 16 vertices....)
• Wilson ch.1 questions (we'll discuss on Thursday)