Networks as pipes. The spread of any epidemic depends on the number of secondary cases per infected case, known as the reproductive rate R0. C P X Y Why do networks matter? Two fundamental mechanisms: Connections example Isolated visionWhy do networks matter? Connected visionWhy do networks matter? Provides food for Romantic Love Bickers with Why do networks matter?

Two fundamental mechanisms: Positions Positional network mechanisms : Networks matter because of the way they capture role behavior and social exchange. Networks as Roles. The unit of interest in a network are the combined sets of actors and their relations. We represent actors with points and relations with lines. Conceptually, almost all of the techniques and measures we describe can be generalized across data format, but you may have to do some of the coding work yourself….

We can examine networks across multiple levels: 1 Ego-network - Have data on a respondent ego and the people they are connected to alters. A good network drawing allows viewers to come away from the image with an almost immediate intuition about the underlying structure of the network being displayed. However, because there are multiple ways to display the same information, and standards for doing so are few, the information content of a network display can be quite variable. Now trace the actual pattern of ties.

- Its All About Change: The Greatest Challenge to Create a Golden Future for Humanity.
- General Topology: Chapters 1–4;
- GitHub - aronlindberg/Social-Network-Analysis-in-R: Social-Network-Analysis-in-R;
- Millers Luck.

You will see that these 4 graphs are exactly the same. Consider the 4 graphs drawn at right. After asking yourself what intuition you gain from each graph, click on the screen. Social Network Data Graph Layout teaser Network visualization helps build intuition, but you have to keep the drawing algorithm in mind. Here we show the same graphs with two different techniques: Tree-Based layouts Most effective for very sparse, regular graphs.

Very useful when relations are strongly directed, such as organization charts or internet connections.

Spring embedder layouts Most effective with graphs that have a strong community structure clustering, etc. Provides a very clear correspondence between social distance and plotted distance Two images of the same network good Fair - poor Social Network Data Graph Layout In general, graphs are cumbersome to work with analytically, though there is a great deal of good work to be done on using visualization to build network intuition. I recommend using layouts that optimize on the feature you are most interested in. The two I use most are a hierarchical layout or a force-directed layout are best.

Social Network Data Social network data are substantively divided by the number of modes in the data. All the nodes are of the same type people, organization, ideas, etc. Examples:Communication, friendship, giving orders, sending email. This is commonly what people think about when thinking about networks: nodes having direct relations with each other. Examples: People as members of groups People as authors on papers Words used often by people Events in the life history of people The two modes of the data represent a duality: you can project the data as people connected to people through joint membership in a group, or groups to each other through common membership There may be multiple relations of multiple types connecting your nodes.

Bipartite networks imply a constraint on the mixing, such that ties only cross classes. Here we see a tie connecting each woman with the party she attended Davis data By projecting the data, one can look at the shared between people or the common memberships in groups: this is the person-to-person projection of the 2-mode data. Social Network Data Basic Data Elements: Modes By projecting the data, one can look at the shared between people or the common memberships in groups: this is the group-to-group projection of the 2-mode data.

Social Network Data Example of a 2-mode network: faculty supervising students - Any list of what people do — meetings, clubs, activities, co- authorship, — that they do with others forms network data. Moody Casalino, Lawrence P. Pesko, Andrew M. Ryan, David J.

Nyweide, Theodore J. From pictures to matrices a b c e d Undirected, binary a b c d e a b c d e 1 1 1 1 1 1 1 1 1 1 An undirected graph and the corresponding matrix is symmetric. Because network images are hard to work with, we often use an adjacency matrix to represent the network. The matrix X at right represents an undirected binary network. Each node a-e is listed on both the row and the column. The ith row and the jth column Xij records the value of a tie from node i to node j.

For example, the line between nodes a and b is represented as an entry in the first row and second column red at right.

## Social Network Analysis: An Introduction

Because the graph is undirected the ties sent are the same as the ties receive, so every entry above the diagonal equals the entries below the diagonal. Directed, binary a b c e d a b c d e a b c d e 1 1 1 1 1 1 1 A directed graph and the corresponding matrix is asymmetrical. Directed graphs, on the other hand, are asymmetrical. From matrices to lists binary a b c d e a b c d e 1 1 1 1 1 1 1 1 1 1 a b b a c c b d e d c e e c d a b b a b c c b c d c e d c d e e c e d Adjacency List Arc List Social network analysts also use adjacency lists and arc lists to more efficiently store network data.

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One can get either projection easily with a little matrix multiplication. First define AT as the transpose of A simply reverse the rows and columns. Basic Volume Measures Social Network Data Degree: Number of links adjacent to a node a b c d e a b c d e 1 1 1 1 1 1 1 1 1 3 0 2 1 2 1 2 1 7 Basic Volume Measures Social Network Data Weighted Degree: Sum of links adjacent to a node a b c d e a b c d e 1 1 2 3 1 5 1 1 1 6 0 6 1 3 5 4 1 14 For example only 3.

Similarly, only 1.

This figure represents the distribution of cases across that space, with key points labeled. The regression estimates define a simple 2-d space of slope Y and intercept x. But even stronger use among those with decreasing substance use. Mental health and network size Network size matters for depressive symptoms, but not linearly Falci, Christina, and Clea McNeely. Health benefits of network growth The risk of functional impairment among older adults decreases as they have more confidants in their personal networks Predicted probabilities of different degrees of functional impairment among older adults, by the number of confidants added Cornwell, Benjamin, and Edward O.

This can only be true if there is a chain of contact from one actor to another.

## Social Networking eBooks

Measuring Networks: Connectionist properties One actor can reach another if there is a path in the graph connecting them. On a path, you never go backwards or revisit the same node twice. Reachability If you can trace a sequence of relations from one actor to another, then the two are reachable. If there is at least one path connecting every pair of actors in the graph, the graph is connected and is called a component. Intuitively, a component is the set of people who are all connected by a chain of relations. Measuring Networks: Connectivity Reachability This example contains many components.

Because relations can be directed or undirected, components come in two flavors: For a graph with any directed edges, there are two types of components: Strong components consist of the set s of all nodes that are mutually reachable Weak components consist of the set s of all nodes where at least one node can reach the other.

There are only 2 strong components with more than 1 person in this network. Components are the minimum requirement for social groups. As we will see later, they are necessary but not sufficient All of the major network analysis software identifies strong and weak components Measuring Networks: Connectivity Reachability Since hubs are rare, PA networks are robust to random attack, but very fragile to targeted attack.

Measuring Networks: Connectivity Distance Calculating distance in global networks: Powers of the adjacency matrix Calculate reachability through matrix multiplication. Calculating distance in global networks: Breadth-First Search In large networks, matrix multiplication is just too slow.

## Social Network Analysis for Startups by Alexander Kouznetsov, Maksim Tsvetovat

A breadth- first search algorithm works by walking through the graph, reaching all nodes from a particular start node. Distance is calculated directly in most SNA software packages. The diameter of a graph is the longest geodesic, giving the maximum distance. We often use the l, or the mean distance between every pair to characterize the entire graph. For example, all else equal, we would expect rumors to travel faster through settings where the average distance is small.

We can modify the random equation by adjusting a, such that some portion of the contacts are random, the rest not. Measuring Networks: Connectivity Redundancy Local Density is the proportion of pairs tied, excluding ego. Transitivity is the proportion of two-step ties that are closed Friend of a Friend is a friend Density Transitivity Transitivity No ego 0 0 0 0.

Centrality refers to one dimension of location, identifying where an actor resides in a network. The framework is divided into three stages; sampling, data processing and inference. Methodology in each stageis noted as data collection, data mining and statistical analysis. Three different types of sampling methods are proposed in the literature, simple random sampling and star snowball sampling Kolaczyk, Network analysis is applicable to different types of data. Subject human or animal to subject interactions or connections and data mapping or graphing and hence the development of the adjacent matricesisstraightforward.

In which situation the researcher can skip the 1st step of entry recognition, deletion, stemming and thematic coding data preprocessing step and move to the next step of identification and validity and reliability checking Figure 3. However, concepts mapping for information exchange, gene expression and protein interactions arerelatively complicated and require additional steps prior to development of numerical coding to form data matrices. Henceforth these data are knows as text data and the type of analyses is known as text analysis or text mining.

When network data are collected in terms of quantitative measurements then the text mining step that I explain next can be skipped.

In each field, there are algorithms proposed to obtain data coding and this is beyond the scope of this chapter. The systematic process in the analytical framework described in this section involveshypothetical applications and discussion on sample results. The methods describe in this chapter is in line with content analyses and data coding that uncover themes and categories using concept mapping and text mining.

Social network analytical framework described herein is summarized in Figure 3. Data mining software uses the following four steps of preprocessing, named entity recognition, deletion, stemming and thematic coding, which is done by thesaurus creation and application Yong et. The notion of text mining is also known as concept driven extraction and visualization framework Jahiruddin, et. Namedentity recognition is the most crucial step in initial data preprocessing. This step is similar to the identification of cliques or similar groups also known as clusters and needs the prior knowledge of the subject area of research.

Named entity recognition in bioinformatics applications is similar to the concept of comparative analysis of gene clusters where known gene clusters are matched or mapped with the common coding using the ancestral relationships Song, et. Song et. In other social network analyses applications, a sample of documents for example gene sequences or text data are scanned to recognize the pertinent entities and these entities called clusters or themes are entered into the data mining software as attributes or clusters.