This project is a product of Mürsel Taşgın's PhD study under the supervision of Haluk O. Bingöl

You can directly contact to Mürsel Taşgın for inquiries about this study.

### Abstract

In this work, we analyze gossip spreading on weighted networks. We try to define a new metric to classify weighted complex networks using our model. The model proposed here is based on the gossip spreading model introduced by Lind et al. on unweighted networks. The new metric is based on gossip spreading activity in the network, which is correlated with both topology and relative edge weights in the network.

The model gives more insight about the weight distribution and correlation of topology with edge weights in a network. It also measures how suitable a weighted network is for gossip spreading. We analyze gossip spreading on real weighted networks of human interactions. Six co-occurrence and seven social pattern networks are investigated.

Gossip propagation is found to be a good parameter to distinguish co-occurrence and social pattern networks.

### Definitions

Let G(V,E) be a network where V and E are the sets of nodes and edges, respectively. N=|V | and M=|E|. The one-neighborhood of node i, denoted by N1(i), is the set of nodes directly connected to i by an edge. The degree of i is ki = |N1(i)|. A victim v is a node who is the subject of a gossip and will suffer from the spread of the gossip. The node which originates the gossip is called the originator r. A spreader s is a node who hears the gossip and furthers it. A target t is a node that is connected to both the victim and the spreader. Then, gossip about a victim is spread in the network from spreader to target which in turn becomes a spreader.

### Gossip is not symmetric

### Discriminating co-occurrence and social pattern networks

Network type plays a key role on gossip spreading. For example, co-authorship networks are formed by people coauthored in the same paper, and for this reason authors of a paper are all connected to each other. Hence it is locally clique-like. So gossips spread mostly through on small paths, i.e. more dense connectivity inside small groups. This is a characteristic property of co-occurrence networks. This can be verified with the parallelism of the clustering coefficient and gossip spread rates in the undirected case, i.e. σ/CC. However face-to-face proximity networks are generally formed by a person in the center and other people know each other through him. The components of these networks are like cascades, that is one person passes to another, rather than fully connected cliques where one person has access to almost all. Although gossip spread rates are very high (around 0.9), clustering coefficient values are lower than ones in co-authorship networks.

Cond-mat 2005 - coauthorship network dataset |
Reuters news co-occurence network dataset |

Socio-patterns Hyper-text 2009 conference dataset |

### Strategies to avoid gossip

According to our model, one can avoid gossip by applying some strategies:- Elimination of triangles reduces the number of friends that can gossip about a victim.
- Elimination of triangle cascades can also reduce the spread. This can be done by having friends from different domains so that a friend from one domain does not know anybody from another domain. Therefore, gossip can spread as far as all the friends of that domain but cannot jump to another domain. As a general rule of thumb, it helps to have islands of friends such that no intra group communication is possible. In real life, we are in communities such as friends from high school, from college, from work. As long as the communities do not overlap, spread of gossip is relatively under control. The observations (1) and (2) are valid for both unweighted and weighted networks.
- In weighted networks, one can control the spread by means of the weights. Gossip does not spread if victim
*v*have closer friendship to his friends*i*and*j*than their friendship to each other,*i.e.**wiv*>*wij*and*wjv*>*wji*. In a directed weighted network, this has an interesting consequence: What your friends thinkof you is more important than what you think of them, i.e.*wiv*versus*wvi*.