Problem 1 Consider network 1. The dashed lines are weak ties and the solid lines are strong ties. Pink and white represent female and male. a) Is the graph connected? b) How many connected components are there? c) How many giant components does the graph have? d) How many paths of length 8 exist? e) Perform the breadth-first search for node 4. f) Draw the distribution of distances of any two podes for this graph. g) Does the small-world phenomenon hold for this 11 graph? n) What is the clustering co-efficient of nodelp i) List all local bridges. Figure 1: Network 1 1) What is the span of the edge 34? k) Does node 4 satisfy the Strong Triadic Closure Prop- erty? 1) What are the minimum and maximum embeddedness in the graph? 2 m) State the Homophily test according to gender in this net- work. n) Is there evidence of homophily? o) Draw another snapshot of the network where in addition to the existing links, (5,7). (9.10), (2,5) are formed. p) Which of the above three links form a closure and of what Figure 2: Network 2 erty? 5 1) What are the minimum and maximum embeddedness in the graph? m) State the Homophily test according to gender in this net- work. n) Is there evidence of homophily? o) Draw another snapshot of the network where in addition to the existing links(5.7). (9.10), (2,5) are formed. I p) Which of the above three links form a closure and of wlt type? Figure 2: Network 2 q) To track the link formation in the two snapshots, derive T (k) and plot it as a function of k. r) According to the graph in q). when two individuals are most probable to become friends? s) Back to the original network, is it possible to label the unlabeled links with + and -'s so that the network becomes balanced? (although the network is not completely connected, you can still use the Structural Balance Property) t) Is it possible to label the unlabeled links with + and -'s so that the network becomes weakly balanced but not balanced? u) Consider Network 2, where the edges are removed and the nodes are located on a grid. Perform two rounds of movement for the segregation model with threshold t=2, where the unsatisfied agents are scheduled to move by considering them one row at a time working downward through the grid, and each agent moves to the nearest cell that will make it satisfied. 120 DEEBA