Murtaza Abbas Asad Ali

NETWORKOLOGY THE SCIENCE OF NETWORKS

So How Do You Explain A Science ?... Hmmmm……

Definition !!! Here is the definition

Network Theory Definition Network theory is an area of applied mathematics and network science and part of graph theory. Network theory concerns itself with the study of graphs as a representation of either symmetric relations or, more generally, of asymmetric relations between discrete objects. REF:

WHAT WOW PARDON HUH !?! OKaaaay!! LOLZ !! Excuse ME…

What Is Network Theory ? -It is the science of Networks -It Studies Networks using Math Models

Where Is It Applied/Used ? What Questions Does it Answer ?

Application 1 In a successful two-year pilot program, social workers asked these HIV-positive people to contact others in their social networks and encourage them to get tested.

Application 2 Saddam Hussain’s capture (as stated by the video in the resource slide) was made possible by using network analysis.

Application 3 Ref:

And There Are Many More… Check out the wiki for further reference

Network Theory In-Detail Theory of Network Theory

Network Theory Content (By network it means any type of network) Network Optimization Network Analysis

Network Optimization Trying to find the optimal way of completing a task

Network Analysis By Network Type – Social Network Analysis – Biological Network Analysis (Not included In Presentation) By Analysis Type – Link Analysis – Centrality Measure Analysis

Link Analysis Link analysis is a subset of network analysis, exploring associations between objects, when relationships between many objects have to be analyzed USAGE – Banks and insurance agencies in fraud detection – Search engines for relevance rating

Centrality Measures Degree of Centrality Of Node: A node is central based on its number of connections Ref:

Centrality Measures Degree of Centrality Of Node: Shows the probability or risk of receiving or catching something going around the network. A high centrality degree is called “Hub” Incase of 2-way communication (Friendship): - In-degree = Popularity - Out-degree = Socializing Ref:

Centrality Measures Clique: A group where each node is connected to every other node Ref:

Centrality Measures Clique: Shows that a group of people have similar characteristics Are formed within institutional networks mostly Ref:

Centrality Measures Eigenvector Centrality: A node is central to the degree it is connected to other central nodes Ref:

Centrality Measures Eigenvector Centrality: “I know a few people who know many people, so I don’t need to know many people.” As important as the central nodes connected to it. Many of these can lead to an fragile network. Ref:

Centrality Measures Betweenness Centrality: A node which connects two sub networks or isolated nodes to the rest of the network. Ref:

Centrality Measures Betweenness Centrality: - Influences flow of information greatly…(Router) - Weak point of network as well - Occurs a lot in short-cuts between nodes Ref:

Centrality Measures Closeness Centrality: A node which has the shortest distance from all the other nodes. Ref:

Centrality Measures Closeness Centrality: They have the best knowledge of what is flowing in the network Ref:

Centrality Measures Others Include: – Network Centralization – Network Reach – Boundary Spanners – Peripheral Players All the mathematical models of the measures explained before are available on Wikipedia... Ref:

Social Network Theories and Properties The Important Part

Social Network Analysis Granovetters theory of strength of weak ties. This theory states that an individual's social network, specifically those who are only acquaintances are better at helping the individual obtain employment than are close personal friends or family. Ref:

6 Degrees Of Separation “Each node in a network is six or less nodes away from the other nodes” Implies the speed with which information travels a network Ref:

Network Transitivity or Clustering The friend of YOUR friend = YOUR Own Friend (LIKELY… but not always) Ref:

Other Properties Include Network resilience Degree distribution Ref:

Degree distribution The degree of a node in a network is the number of links connected to that node. We can define a probability pk to be the fraction of nodes in the network that have degree k. Meanwhile, the pk could be considered as an uniform probability for choosing nodes with degree k at random. Plot pk (vertical axis) with degree k (horizontal axis) for some networks can form a histogram of degree distribution of nodes, as follows. Ref:

Ref:

It is observed that the degrees of nodes are highly right-skewed. In other words, the distribution has a long right tail, or heavy-tailed distribution, it might be the well-known long tail effect. Alternatively, this distribution can be plotted in a logarithmic method, as follows. Marvellously, it is nearly conformed with Power law, which is the primary property of scale-free network. In contrast to the Poisson distribution of random graph (Erdős-Rényi model).long tail effectPower lawscale-free networkPoisson distribution random graphErdős-Rényi model Ref:

Network resilience The resilience of network means the removal of its nodes, which is related to the concept of degree distributions. The function and structure of a network usually rely on its connectivity. Once some nodes are removed, the length of paths could be increase, even the network becomes disconnected. However, there are a different ways to remove the nodes. One way to remove the nodes in a network is to random removal. This approach wouldn't affect the distances between nodes almost since most nodes in a network have low degree and therefore lie on few paths between others. The other way to remove nodes from networks is targeted at high- degree nodes. Needless to say, it will have tremendous effects on the structure of a network. And the distance would increase acutely with the fraction of nodes removed. The following picture can explan it! (Note blue for random removal and red for high-degree removal.) Ref:

Conclusion We covered: – What is network theory – What network theory deals with – Some implications of network analysis – What are the centrality measures – Some properties and theories regarding social network analysis

THANK YOU For Further Information Please check out the Wiki….. There are even partially viewable books on social network analysis on it.