Summary: PHYS 597A, CMPSC 497E, Graphs and Networks in
Homework 8, due Tuesday Nov. 3
1. Perform a topological analysis of the network below. Consider that edges terminating
in edges are directed toward the endpoint of the edge (e.g. the edge from Th2 related
cytokines is directed toward Th2 cells). For points (a)-(c) you can disregard the sign of
the edges (but not their direction!) and the two autoregulatory loops.
(a) What is the in and out-degree distribution of the network?
(b) Is the network strongly connected? If not, find the largest strongly connected
component, and the in/outcomponents of the strongly connected component.
(c) What is the average distance between the nodes of the largest strongly connected
(d) Give examples of network motifs and interesting subgraphs. Now you can take into
account the edge signs.
(e) In your assessment, which nodes or edges play the most important role in the
connectivity of the network?
2. Now turn the topological analysis into a pseudo-dynamic one. Assume that initially
only the node Bacteria is active. When a node is active, all its edges are also active.
Assume that in order to activate a node at least half of the edges that activate it must be
active, but even one active inhibition will inactivate the node regardless of the presence