let $n$ be any positive integer and let $f_n$ be the friendship (or dutch windmill) graph with $2n+1$ vertices and $3n$ edges. here we study graphs with the same adjacency spectrum as the $f_n$. two graphs are called cospectral if the eigenvalues multiset of their adjacency matrices are the same. let $g$ be a graph cospectral with $f_n$. here we prove that if $g$ has no cycle of length $4$ or $...

Online Social Networks (OSN) during last years acquired a huge and increasing popularity as one of the most important emerging Web phenomena, deeply modifying the behavior of users and contributing to build a solid substrate of connections and relationships among people using the Web. In this preliminary work paper, our purpose is to analyze Facebook, considering a significant sample of data re...

Feld’s friendship paradox states that “your friends have more friends than you, on average.” This paradox arises because extremely popular people, despite being rare, are overrepresented when averaging over friends. Using a sample of the Twitter firehose, we confirm that the friendship paradox holds for >98% of Twitter users. Because of the directed nature of the follower graph on Twitter, we a...

An L(2, 1)-labeling (or distance two labeling) of a graph G is a function f from the vertex set V (G) to the set of all nonnegative integers such that |f(x) − f(y)| ≥ 2 if d(x, y) = 1 and |f(x) − f(y)| ≥ 1 if d(x, y) = 2. The L(2, 1)-labeling number λ(G) of G is the smallest number k such that G has an L(2, 1)-labeling with max{f(v) : v ∈ V (G)} = k. In this paper we completely determine the λ-...

This work analyzes friendship network from aMassively Multiplayer Online Role-Playing Game (MMORPG). The network is based on data from a private server that was active from 2007 until 2011. The work conducts a standard analysis of the network and then divides players according to different groups based on their activity. Work checks how friendship network can be correlated to the clan (a self-o...

The goal of this paper is to investigate the interaction between social ties and deceptive behavior within an experimental setting. To do so, we implement a modified sender-receiver game in which a sender obtains a private signal regarding the value of a state variable and sends a message related to the value of this state variable to the receiver. The sender is allowed to be truthful or to lie...

Social networks have been around since the dawn of civilization. What is unique about social networks today is that a large part of these social networks is computer-mediated. Computer-mediated friendship networks (CMFNs) are a prime example of IT that matters. This research-in-progress focuses on the antecedents to CMFN usage based on Self-Determination Theory and Socio-Emotional Selectivity T...

We study stable matching problems in networks where players are embedded in a social context, and may incorporate friendship relations or altruism into their decisions. Each player is a node in a social network and strives to form a good match with a neighboring player. We consider the existence, computation, and inefficiency of stable matchings from which no pair of players wants to deviate. W...

We analyze a network formation model where agents belong to different communities. Both individual benefits and costs depend on direct as well as indirect connections. Benefits of an indirect connection decrease with distance in the network while the cost of a link depends on the type of agents involved. Two individuals from the same community always face a low linking cost while the cost of fo...