Can probably explain in layman's terms to someone less knowledgable :

1, 2 (sort of, measure what?), 4 power law, 5, 6, 7, 10, 11, 12, 13,

Lost me - or maybe I just don't know the terminology

3, 4 (3 degree distributions), 8 (is there anything different from a network?), 9 (not in this context), 14, 15, 16

i know lots about all but the last 2

Well I got a grand total of 3 responses which is not a terribly encouraging indicator of how many of you all are paying attention. But the few of you who did reply did seem to know most of this already, so on the other hand that's a good indicator of where we all are. On with the answers, the best I can do with them anyway. In the original I accidentally listed two questions as "4", I fixed that in this version. As I said before, I'm trying to establish a common ground, a starting point for us to move forward with in discussing this stuff.

Tim

1) Define "network" - A network is any system where entities (called "nodes") are connected to each other in any fashion (called "links"). Both nodes & links can be composed of real objects, concepts or simply purely mathematical structures. Whatever their actual makeup, two networks that have the same exact structure will always behave exactly the same in a mathematically predictable fashion. Therefore, if you can uncover the structure of any network & find the equations to describe it you can predict what it will do & also how it will react if you change it.

2) How do you measure a network? The most common & basic method of measuring a network is its topology, which is an equation describing the probability distribution of connectivity between the nodes. In other words, you plot a graph with number of links each node has on one axis & number of nodes that have that number of links on the other. The probability function that best fits that plot is called its topology. Common topologies include random (also called normal or Gaussian - see en.wikipedia.org/wiki/Gaus...stribution ), which looks like a bell curve; power-law, scale-free, log-normal & small-world (all covered below; some of these are non-exclusive, ie a network can be both scale-free & small-world). The analytical tool used to measure topology is statistics, comparing which equation comes closest to describing the actual plot of the graph. Beyond the basic topology there are other properties that can be measured, for instance the strength & direction of links, average path length between two random nodes, various aspects of clusters, etc.

3) What is a log-log plot? A log-log plot is one that uses a logarithmic scale on both X & Y axes, in other words from 0 the first group of units is 1-10, the second set is 10-100, the third set is 100-1000, etc. Because several of the equations used in network topology include logarithms, log-log plots are a useful tool in measuring networks.

4) What is a power law? A power law is any function that fits y=ax^k where -a is a constant that equals the rise & k is the slope of the straight line formed by the function in a log-log plot. See en.wikipedia.org/wiki/Powe...stribution for more info.

5) Name 3 degree distributions - Normal/random/Gaussian, power-law, log-normal (see Log-normal distribution , I won't try to summarize), small-world, scale-free, Apollonian.

6) Define "scale-free" - A scale-free network is one that has no sense of "scale" that can be determined by examining local conditions from any vantage point within the network. In other words, if you measure the connectivity of the nodes around you & plug the numbers into a plotting calculator, you can't tell whether you're way out at the edge of the network or deep in the middle of it by comparing the ratio of the more-connected nodes to you vs you to the less-connected ones. That's where the importance of the power-law's straight line log-log plot comes in. In a random network you can tell where you are because the slope changes depending on where you are along the line of the graph. But a power-law graph plots the same slope no matter where you are, so you have no sense of scale. Hence, scale-free. Power-law & scale-free are generally used interchangably. See

7) Define "small world" - A small-world network is one where there's a small "distance" between any two nodes in a network, measured by the shortest path of links connecting them. See en.wikipedia.org/wiki/Smal...ld_network

8) What is a random network? Random=normal=Gaussian=bell curve. When you randomly choose which nodes get connected to which other nodes, the graph that results is a bell curve.

9) What is a graph? In network terms, a graph is a plot of the equation describing the distribution of links between the nodes. Mathematically speaking, Network Theory is a subset of Graph Theory. See en.wikipedia.org/wiki/Graph_theory

10) What is a lattice? In network terms, a lattice is a network where every node is connected to every other node. It's a useful starting point for some network models.

11) What's an Erdos number? Paul Erdos was an important mathematician, the founder of Graph Theory. An Erdos number is the shortest path between you & Erdos, using co-authorship of math papers to build a network. If you co-authored a paper with him, your Erdos number is 1. If you published a paper with someone whose Erdos number is 1, your Erdos number is 2. Erdos himself has an Erdo number of 0. It's an inside joke of sorts for mathematicians & also a useful example of a network to measure. I've never published any papers so I have no Erdos number. See en.wikipedia.org/wiki/Erdos_number

12) What is Zipf's Law? Zipf's Law is a rule that says the distribution of words in a text follows a power-law. It's a very useful concept for computational linguisitics & natural language programming, because you can assign a probability to each word. Not directly network related unless you think of a piece of text as a network of words. See en.wikipedia.org/wiki/Zipf%27s_law

13) What is Pareto's Law? Also called the 80/20 rule. It says that 80% of the results in certain systems come from 20% of the causes & 80% of the remaining results comes from 20% of the remaining causes. When you plot it out on a graph, a power law function appears. See en.wikipedia.org/wiki/Pareto%27s_law

14) What is a bipartite network? Networks don't have to be made up of all one type of node or link. A bipartite network is one made up of two types of nodes. Here's a good depiction of a bipartite network: www.nap.edu/books/030908...ag2570001.jpg A-K are one type of node & 1-4 are another; for instance, actors & movies they appeared in. It's a useful alternate way of thinking about networks, that shows structures that'd be hard to visualize in the standard way.

15) What is the SIR model? Stands for Susceptible, Infected, Recovered. A common model for epidemiology, classifying nodes by whether they can catch the disease, already have it or already got it & can't catch it again. Because epidemics spread through networks, it's very useful to be able to model networks if you're going to track or predict the spread of a disease (or any other phenomenon that acts like one). See en.wikipedia.org/wiki/SIR_Model

16) Define "percolation threshold" - In network terms, percolation means the spread or diffusion of something through a network. The percolation threshold is the point in the process where a percolating cluster, which is a single cluster that can cause the entire network to be infected, appears. Below the percolation threshold there's no possibility of the whole network being infected, although there can be persistent & continued outbreaks in certain areas.

17) Define "information cascade" An information cascade is a concept in social network analysis where a number of people take an action based on someone else taking that action before them. Also called herd behavior. The idea is that only the first person is really making a decision & all the others are relying on his judgement, whether they realize it or not. See en.wikipedia.org/wiki/Info...on_cascade