Networks Are Everywhere

Where is the Naval Postgraduate School? 2 Military graduate school (Navy, Army, Airforce, Marines, international Officers)

Networks Are Everywhere What do we think of when we hear the word “network?” What is a network, really? Into what kinds of problems do network models help us gain insight? Relationship between networks and complexity theory Dr. Ralucca Gera, Professor of Mathematics Project Manager Network Science Academic Certificate Associate Provost for GradEd rgera@nps.edu

Networks Why study networks? https://www.youtube.com/watch?v=UkxDhXWpb4Q How are networks used? https://www.youtube.com/watch?v=vVJcVLQ7O3o (epidemics, biology): https://www.ted.com/talks/nicholas_christakis_how_social_networks_predict_epidemics (maps, places, big data): https://www.youtube.com/watch?v=kQbBQCpVa8s

https://lostcircles.com/ What is a Network? http://www.opte.org/maps/ The Opte Project - visualizing the Internet - Asia: Red; Europe: Green; North America: Blue; Latin America: Yellow; IPs: Cyan; Unknown: White The Internet Most people think of these when they think of networks: Ego-Facebook https://lostcircles.com/ Using the Chrome browser, download the plugin and you can see your network, too!

But Wait, There’s More! Let’s list a couple more examples we think of when we think of networks. What structures do they have in common? Entities Relationships between entities Data describing the entities and/or relationships Key difference between graphs and networks Now, with this expanded understanding of what networks are, let’s list a couple more G = (V,E)

But Wait, There’s (still) More! Since we were young, what is the technique we most often use to solve big, nasty, complicated problems? What is the difference between “complicated” and “complex?” Car parts as set vs. as a car We live in complex times. Complex problems and complex systems resist reductionism and disaggregation. Networks “embrace the complexity” through accounting for connections. Now that we more fully understand the breadth of what may be appropriately modeled by a network, are there any examples we may have missed? What can not be modeled by a network? Networks are the building block of life and our environment. UNCLASSIFIED

Networks: “Flat” or Multilayer? Take the idea of a social network and expand. When we include the networks associated with each element of an environment, we come closer to characterizing the environment than using one single layer or a simple aggregation of those single layers. What problem are you trying to solve?

Applications: Targeting A military example, High Payoff Targeting: Why was the network of bad actors largely unaffected even though I removed the (apparently) most important guy from the network? That social network is only a part of the enemy’s ecosystem. We didn’t account for the impact of those other elements on the network’s robustness. Network analysis of the environment lends greater context and texture to the decision making environment, enabling greater detail and predictive power in decision recommendations.

Applications: Pandemic Spread Dirk Brockmann, and Dirk Helbing Science 2013;342:1337-1342 Pandemic mitigation must account for “effective distance,” rather than geographic distance in today’s connected world.

Networks and Obesity https://www.coursera.org/learn/systems-science-obesity/lecture/92Q5g/obesity-social-networks Obesity clusters in children’s and adults social networks. Having a social connection who is obese predicts obesity.

Application: Job Hunting 1 An ego-LinkedIn Network 474 vertices and 5263 edges 8 communities identified by Gephi Average degree is 22 Average distance in the graph is 3 Network diameter is 9 One of the vertices is the only one that has connections to three communities. Three times “more important” than the next highest vertex.